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# 10–6 The materials price variance can be computed at what two different points in time? Which...

10–6    The materials price variance can be computed at what two different points in time?

Which point is better? Why?

10–7    If the materials price variance is favorable but the materials quantity variance is unfavor- able, what might this indicate?

## Related Questions in Managerial Accounting

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December 07, 2015

. . . . . . . . . . 10.00 Total cost per timing device . . . . . . . . . . . . . . . . . . . . $69.75 The manager of the Clock Division feels that she can ’t quote a price greater than$70 per timing device to the oven manufacturer if her division is to get the job

• ### Refer to the data in Exercise 11—8. Assume that instead

(Solved) July 12, 2016

Refer to the data in Exercise 11—8. Assume that instead of producing 4,000 units during the month, the company produced only 3,000 units, using 14,750 pounds of material. (The rest of the material purchased remained in raw materials inventory.) Required: Compute the direct materials price

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In middle East countries, we can consider the product refining of crude oil for discussion. The refining of crude oil is having standard components and standard process. The crude oil is...
• ### CASE 11A–7 Transfer Pricing; Divisional Performance [LO5] Stanco, Inc., is a decentralized...

December 07, 2015

. . . . . . . . . . 10.00 Total cost per timing device . . . . . . . . . . . . . . . . . . . . $69.75 The manager of the Clock Division feels that she can ’t quote a price greater than$70 per timing device to the oven manufacturer if her division is to get the job

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(Solved) 4 weeks ago

, their level e.g. manager, trainee and the type of business in which they are employed e.g. government, education, small private firm; Body of the report answering the questions you have devised broken up into the two areas; Your reflections on the similarities and differences in expectations

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Factoring Equation 2i^2+4i-15 using quadratic formula

Use the Factor quadratic calculator below to do your conversion.

Factoring 2i^2+4i-15 Solution

Factoring quadratic equation 2i^2+4i-15

The variable we want to find is i

We will solve for i using quadratic formula -b +/- sqrt(b^2-4ac)/(2a), graphical method and completion of squares.

Solving Using Quadratic Formula

${x}_{}=\frac{-b±\sqrt{{b}^{2}-4ac}}{2a}$

Where a= 2, b=4, and c=-15

Applying values to the variables of quadratic equation -b, a and c we have

${i}_{}=\frac{-4±\sqrt{{4}^{2}-4x\mathrm{2x}\mathrm{-15}}}{2x2}$

This gives

${i}_{}=\frac{-4±\sqrt{{4}^{2}-\mathrm{-120}}}{4}$

${i}_{}=\frac{-4±\sqrt{136}}{4}$

${i}_{}=\frac{-4±11.6619037897}{4}$

${\mathrm{i1}}_{}=\frac{-4+11.6619037897}{4}$

${\mathrm{i2}}_{}=\frac{-4-11.6619037897}{4}$

${i}_{1}=\frac{7.66190378969}{4}$

${i}_{1}=\frac{-15.6619037897}{4}$

The i values are

i1 =   1.91547594742 and i2 =   -3.91547594742

Factoring Quadratic equation 2i^2+4i-15 using Completion of Squares

2i^2+4i-15 =0

Step1: Divide all terms by the coefficient of i2 which is 2.

${i}^{2}+\frac{4}{2}x-\frac{15}{2}=0$

Step 2: Keep all terms containing x on one side. Move the constant to the right.

${i}^{2}+\frac{4}{2}i=\frac{15}{2}$

Step 3: Take half of the x-term coefficient and square it. Add this value to both sides.

${i}^{2}+\frac{4}{2}i+{\left(\frac{4}{4}\right)}^{2}=\frac{15}{2}+{\left(\frac{4}{4}\right)}^{2}$

Step 4: Simplify right hand sides of expression.

${i}^{2}+\frac{4}{2}i+{\left(\frac{4}{4}\right)}^{2}=\frac{136}{16}$

Step 2: Write the perfect square on the left.

${\left(i+\frac{4}{4}\right)}^{2}=\frac{136}{16}$

Step 2: Take the square root on both sides of the equation.

$i+\frac{4}{4}=±\sqrt{\frac{136}{16}}$

Step 2: solve for root i1.

${i}_{1}=-\frac{4}{4}+\frac{11.6619037897}{4}=\frac{7.66190378969}{4}$

${i}_{1}=1.91547594742$

Step 2: solve for root i2.

${i}_{2}=-\frac{4}{4}-\frac{11.6619037897}{4}=\frac{-15.6619037897}{4}$

${i}_{2}=-3.91547594742$

Solving equation 2i^2+4i-15 using Quadratic graph

 i2 + i + = 0
 Solutions

how to factor polynomials?

Polynomials can be factored using this factoring calculator

how to factor trinomials

Trinomials can be solved using our quadratic solver

Can this be used for factoring receivables, business, accounting, invoice, Finance etc

No this cannot be used for that

If you spot an error on this site, we would be grateful if you could report it to us by using the contact email provided. send email to contact on our site.

Other Variants of 2i^2+4i-15 are below

format: plain


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# Correlation between speed, distance, mass, etc between a planet and a star (or moon and planet)?

While playing around with some little scripts, generating solar systems, I started to wonder about the correlation between the different objects. Up until now, distance, mass, size and speed are randomly generated.

Are there any 'common rules' on how some of theese objects correlate? Are planets close to a star always smaller and faster, and planets far away usually larger and slower? Is the rotation speed affected?

And how about the correlations between moons and their planet?

At the end of the day, I'm triyng to make the the generation a bit more accurate / realistic.

Thanks in advance! Sorry for the english, it's a second language for me.

-
There do exist various theories of solar system formation, but with the recent discovery of hoards of exoplanets, many of the accepted principles on which these theories were historically built have been called into question. I assume it is an active field of research and perhaps one of our astronomers can say something about the current state of things. – dmckee Jun 17 '13 at 18:27

I spot two pairs of related quantities in your list.

Speed (I assume you mean orbital speed, not how fast the planet is spinning about its own axis) and distance. The orbital period and the semi-major axis of the orbit are related by Kepler's third law. For a circular orbit, the semi-major axis is the radius (distance) and the period is trivially related to the speed ($v=\frac{2 \pi a}{P}$, where $P$ is the period and $a$ is the semi-major axis). For elliptical orbits the speed changes over the course of an orbit, so the period instead tells you something about the average speed of the planet. Planets with large semi-major axes might move faster than planets with smaller semi-major axes at a particular instant (depending on the eccentricity of the orbits), but averaged over an orbit larger $a$ always means lower average $v$.

Mass and size are also somewhat related, but this is something of a complex topic. More mass means stronger self-gravitation, which tends to compress the size of the planet, but it also means more matter, which tends to grow the size. A planet of a given mass will have a size such that the inward pull of gravity is balanced by the outward pressure supplied by the material making up the planet. For a gas giant/star this is called hydrostatic equilibrium. I'm not sure if there's a similar term for a solid/molten planet but things are complicated somewhat by these condensed phases of matter. If you're trying to come up with a simple model, try picking a mass at random, and look up typical average densities for solid and gas planets. Pick a type of planet then use the average density and the mass to compute the radius.

There is no strong evidence that supports smaller planets typically being closer to their stars than larger planets (which is the case in our solar system); many stars have been seen with gas giants orbiting as close or closer to their star as Mercury is to the Sun. It is generally believed that these gas giants formed further out and migrated inward.

The rotation speed of a planet (about its own axis) is initially fixed by the total angular momentum of the material that collapsed to form the planet. Over time, however, tidal locking can influence the spin of two orbiting bodies. This is why Earth's Moon has period of revolution equal to its orbital period, for instance.

A planet/moon that gets too close to another body with strong tidal forces can be ripped apart.

There can also be favoured/disfavoured distances for orbits due to orbital resonance, or a planet can be entirely ejected from its orbit.

The interaction of a planet and its moon(s) is essentially the same as a star and planet system, unless you expect effects particular to a star to be important (one example would be radiation pressure).

In the end, to get a more realistic simulation going, I'd worry less about initial conditions and more about making sure your method is working accurately and accounting for not only gravitation between the star and the planets but also gravitation between planets and tidal effects as well. If you achieve that, instabilities will make sure that any "unrealistic" scenario will decay into a stable configuration over time (potentially ejecting one or several planets from the system in the process).

-
In re: tidal forces - please also add the constraint on Roche limit. You may also consider adding more stuff on interaction between planets in the paragraph on resonance. – Deer Hunter Jun 17 '13 at 18:53
Added a couple more. This is a pretty broad topic, though, so I had to stop somewhere... Happy to add additional specific examples/phenomena if you have ideas. – Kyle Oman Jun 17 '13 at 19:00
For me at least, it's complete enough so far - That's a lot to work with and I have to thank you for the long answer. I didnt even know of Kepler's law yet, so there's more than enough for me to read into. But it's exactly what I wanted to know – Katai Jun 18 '13 at 7:08


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General Article

International Journal of Sustainable Building Technology and Urban Development. 30 June 2022. 221-230
https://doi.org/10.22712/susb.20220018

# MAIN

• Introduction

• LCCA as a Decision-Making Process

• LCCA Inputs

• Environmental and Social Considerations in LCCA

• LCCA Analysis Methods

• LCCA Case Study

• Interpretation and Implementation of LCCA

• Summary and Conclusions

Introduction

Life Cycle Cost Analysis (LCCA) is used in our daily life to make simple decisions and in the selection of best alternatives in complex infrastructure projects. Regardless of the applications of LCCA, at the end of this process, someone must select the best alternative based on this tool. In this paper, applications and challenges in the application of LCCA for transportation infrastructure projects and more specifically for roads and pavements will be investigated. In many cases, organizations and their engineers conduct LCCA to support and justify their decisions. However, the accuracy and reliability of LCCA outputs depend on many parameters.

A simple model of LCCA is shown in Figure 1. As it can be seen in Figure 1, a LCCA includes input parameters, an analysis method or model, and outputs or ranking of several alternatives. An important step that must be considered is interpretation or validation of results before implementation of LCCA outputs.

### General Life Cycle Cost Analysis Processes.

LCCA as a Decision-Making Process

LCCA can be used for different infrastructure projects such as buildings, bridges, dams, pipelines, pavements, sidewalks, and other assets that their owners or designers should select the best alternative from several options. In the pavement engineering area, LCCA can be applied for the selection of pavement structure for new roads or it can be applied to pavement maintenance and rehabilitation projects to select the best road treatments.

LCCA can be conducted at different stages of a project. For example, it can be used in the planning, design, maintenance, and rehabilitation of an asset. In most infrastructure LCCA projects, it is expected to look at the Whole Life Cycle Cost (WLCC) which includes initial construction costs, costs and times of required maintenance and rehabilitations, and even disposal of the asset. The definition of “whole” in a WLCCA could be different in different industries, for example, in pavement engineering, one common concept of “whole” could be incorporation of all important factors such as energy consumption related to extraction and production of materials, CO2 generation from all project’s activities, and social costs such as users’ delay and even cost of accidents. Incorporating environmental and social costs in an infrastructure project is a challenging task in LCCA as will be explained more in the next sections.

LCCA Inputs

The most important input parameters in any LCCA are costs and service lives of different alternatives. This looks a simple task; however, it will be a complex process for major projects and requires comprehensive investigation and research to find accurate costs and service lives of different materials or alternatives. Initial costs are the highest and most important input parameter which will impact the LCCA results more than the future project’s costs. Some agencies consider the initial project costs as the only project’s cost. This approach might work for some assets when future costs of the project are relatively low; however, for long-term projects that have high maintenance costs, it is not the best methodology. For example, in the selection of best surfacing material (asphalt vs concrete) for a paving project, if only the initial cost is considered, asphalt pavement must be selected for all projects as the initial cost of concrete could be 3 to 4 times more than the initial cost of asphalt; however, if the cost of required maintenance and rehabilitations during the life of a rod are considered, results could change. Municipal agencies use concrete paving for their bus stops or at their intersections as the maintenance cost of asphalt paving is very high at these locations.

### Converting Alternative’ Costs to Net Present Value in a LCCA.

One common question is if the inflation rates must be applied to each future cost of alternative? As prediction of future inflations, during AP in a LCCA, is not possible, the future costs are estimated based on today’s costs.

LCCA analysis methods are classified into deterministic and probabilistic methods. In a deterministic LCCA method, average values of input parameters are considered as the best estimate of them. Using a LCCA method, the output also will be a value for each alternative. As it was discussed before, it is difficult to estimate only one value for LCCA costs and their timelines; therefore, considering a range for each project’s costs and activity times could provide various scenarios for LCCA results. Probabilistic methods, using different computer algorithms, consider a range of values and distribution shapes for each input parameter. Therefore, the output is not a fixed value, but a range of possible scenarios which provides a better tool for the decision maker. Figure 6 depicts a LCCA output for two different scenarios, with and without users’ costs for a typical pavement project (2). Parameters such as the difference in NPV at specific cumulative probability and difference in probabilities at specific NPV, from probabilistic results, can be used for comparison between alternatives (for example 90% probability and \$3.2 M NPV in Figure 6).

### Example of a Probabilistic LCCA Result [2].

LCCA Case Study

To show subjectivities in LCCA results, two case studies are shown from literature. One related comparison between selection of asphalt or concrete for a new road construction. The objective of this comparison is not to say which one is right or wrong, but to show that results of LCCA can change by considering different assumptions.

The first study published by the European Concrete Paving Association (EUPAVE) considered two typical pavement structures paved with concrete and asphalt surfaces. A LCCA was conducted for these two alternatives with a discount rate of 4% and 90 years AP and different assumptions for type and time of maintenance and rehabilitation. Results of NPV from this study are shown in Figure 7. Based on this study a road with concrete surface will be approximately 8.5% less costly than a road with asphalt surface during its life (90 years) with a discount rate of 4%; however, when the discount rate increased to 6%, asphalt alternative was approximately 5% less costly. This study did not consider any GHG and users’ costs [15].

### NPV Results for Asphalt and Concrete Roads by EUPAV [15].

Another European study by Scheving compared the NPV of asphalt and concrete roads in Iceland for different traffic levels. For this comparison, an AP of 40 years and discount rate of 6% were considered. Results are shown in Figure 8. Based on this LCCA, at traffic below 14,000 AADT, concrete pavement was 10% to 15% higher than asphalt; however, concrete was competitive when traffic was higher than 14,000 AADT. This study did not look at any environmental costs, but included the users’ delay costs [16].

### NPV Results for Asphalt and Concrete Roads by Scheving [16].

Interpretation and Implementation of LCCA

There are subjectivities and uncertainties in any LCCA that a designer must be careful about. Some considerations in the application of LCCA for infrastructural projects are summarized below:

⦁The source, accuracy, and reliability of input parameters must be verified.

⦁Generally, more efforts must be made on accurate estimation of higher and earlier costs as they impact the results more.

⦁Historical costs and past performance experiences of agencies could be considered in LCCA processes; however, they must be reviewed and revisited frequently to reflect the real world conditions.

⦁Probabilistic LCCA models provide a better view of various scenarios for projects’ alternatives than deterministic methods.

⦁Biased or predetermined decisions must be identified and prevented in any LCCA.

⦁Agencies must develop a guide or manual for their LCCA to provide consistency in their LCCA applications.

⦁If LCCA results of various alternatives are very close, other factors such as lower initial cost or shorter construction time can be considered as the best alternative.

⦁In addition to LCCA results, other project management considerations such as risk evaluation, quality control and assurance, complexity of alternatives, project’s delivery and payment methods, and performance-based construction specifications must be considered in the selection of the best projects’ alternatives.

Summary and Conclusions

LCCA is a decision supports tool that prioritizes different alternatives for infrastructure projects. Selection and accuracy of input parameters are important steps in conducting a LCCA. The new trends in transportation infrastructure is to consider environmental and social and users’ costs in LCCA. Challenges in considerations of environmental impacts and user costs for pavement projects were discussed. This paper attempted to review important factors in LCCA and to bring attention to subjectivities and uncertainties in LCCA.

## References

1
F. Gu and N. Tran, Best Practices for Determining Life Cycle Cost of Asphalt Pavements. 2019, National Center for Asphalt Technology-NCAT Report 19-03, Auburn, AL.
2
Manu Diependaele, A Guide on the Basic Principles of Life-Cycle Cost Analysis (LCCA) of Pavements. 2008, Published by European Concrete Paving Association, Brussels.
3
Ontario Hot Mix Producers Association, Carbon Footprint: How Does Asphalt Stack Up? [Online], 2010. Available at: http://www.onasphalt.org/files/factsheets/Carbon%20Footprint_How%20Does%20Asphalt%20Stack%20Up.pdf. [Accessed 5/2022].
4
Portland Cement Association, Roadmap to Carbon Neutrally [Online], 2021. Available at: https://www.cement. org/docs/default-source/cement-concrete-applications/pca_roadmap-to-carbon-neutrality_jan-2022.pdf?sfvrsn=33d8fcbf_2. [Accessed 5/2022].
5
Government of Canada. The Federal Carbon Pollution Pricing Benchmark [Online], 2019. Available at: https://www.canada.ca/en/environment-climate-change/services/climate-change/pricing-pollution-how-it-will-work/carbon-pollution-pricing-federal-benchmark-information.html[Accessed 5/2022].
6
A. Sha, R. Lin, Y. Huang, and C. Wang, Greenhouse Gas Emissions from Asphalt Pavement Construction: A Case Study in China. Int. Journal of Environ. Research Public Health. 13(3) (2016), pp. 351. Published online, 22. doi: 10.3390/ijerph13030351. 10.3390/ijerph1303035127011196PMC4809014
7
M. Zheng, W. Chen, X. Ding, W. Zhang, and S. Yu, Life Cycle Environmental Assessment of Preventive Maintenance Techniques for Asphalt Pavement. Journal of Sustainability. 13(9) (2021), pp. 4887. Available at: 10.3390/su13094887[Accessed 5/2022].
8
B. Uhlman, J. Andrews, A. Kadrmas, L. Egan, and T. Harrawood, Verification of Eco-efficiency Analysis under NSF Protocol P352 Part B. 2010, a Report Submitted to BASF Corporation.
9
M. Foth and C. Berthelot, Quantifying Greenhouse Gas Generation for Roadway Maintenance, Rehabilitation and Reconstruction Treatments. 2013, Transportation Association of Canada, Winnipeg, Manitoba.
10
J. Walls III and R.S. Michael, Life-Cycle Cost Analysis in Pavement Design, In Search of Better Investment Decisions. 1998, FHWA-SA-98-07, Washington, DC.
11
P. Babashamsi, N.I.M. Yusoff, H. Ceylan, N.G.M. Nor, and H. Salarzadeh Jenatabadi, Evaluation of Pavement Life Cycle Cost Analysis: Review and Analysis. International Journal of Pavement Research and Technology. 9 (2016), pp. 241-254. 10.1016/j.ijprt.2016.08.004
12
S. Rahman and D.J. Vanier, Life Cycle Cost Analysis as a Decision Support Tool for Managing Municipal. 2004, Infrastructure, Institute for Research in Construction, Canadian National Research Council. NRCC-46774.
13
M. Bagdatli, Fuzzy Logic-Based Life-Cycle Cost Analysis of Road Pavements. Journal of Transportation Engineering, Part B: Pavements, American Society of Civil Engineers. 144(4) (2018). 10.1061/JPEODX.0000081
14
A. Asadi, A. Hadavi, and R.J. Krizek, Bridge Life-Cycle Cost Analysis Using Artificial Neural Networks. Proceedings of the 28th International Conference of CIB W78. (2011).
15
M. Diependaele, A guide on the basic principles of Life-Cycle Cost Analysis (LCCA) of pavement. 2018, published by the European Concrete Paving Association (EUPAVE).
16
A.G. Scheving, Life Cycle Cost Analysis of Asphalt and Concrete Pavements. 2011, Master of Science thesis at Reykjavík University. Available at: https://skemman.is/bitstream/1946/7684/1/Life%20Cycle%20Cost%20 Analysis%20of%20Asphalt%20and%20Concrete%20Pavements.pdf. [Accessed 6/2022].


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# Resistor size help for project

#### Wdunlap89

Joined May 21, 2020
4
I apologize in advance because I am mostly electronic illiterate.

I am trying to build a set of inline on/off switches for remote control of 3 microphones using 3 illuminated push button latching DPDT 2NO2NC switches the LED in the switch is rated up to 24v 15mA. I'll be powering the switch LED with an AC 100-240v to DC 12v 3A power supply adapter what I need to know is what size resistor needs to be run in series from the adapter to each of the switches LED from my calculations I think I need 700ohm 36watt. Is this right if so I dont have room for a 7 in long wire wound resistor much less 3 of them.

Also there will not be power going to the microphone from the power supply. Any help would be appreciated and if this is absurd and would never work then harsh criticism is welcomed thanks in advance

Joined Feb 20, 2016
3,528
A diagram would help.
As you will be running the LEDs on 12V, and it sounds like they may have a resistor inbuilt for 24V, no extra resistor is needed.
There is no way a 700 ohm 36 W resistor is needed on 12V.
Just out of interest, please show us how you calculated that and we may be able to assist you.

The LEDs are polarity sensitive so must be connected the correct way to avoid popping them.

#### AlbertHall

Joined Jun 4, 2014
9,873
Does the LED in the switch already have a resistor, some do?
For a standard LED from 12V at 15mA you would use (12V - 2V)/15mA ≅ 680Ω. The power in the resistor would be RI^2 = 680 * 15mA^2 = 150mW.

Joined Feb 20, 2016
3,528
As @AlbertHall indicates, I think adding a 680R resistor in series is a good idea as you may not know if the LEDs do include the resistors or not. The extra resistor will not hurt, but will save the LEDs if they do not have internal ones. And you can measure the current and work out what internal resistor is there. That could be a good excercise for you to try your Ohms law out on.

#### ci139

Joined Jul 11, 2016
1,463
there are many options
• the LED has no limiting resistor and is AC/DC (double reverse parallel)
• the LED has a limiting resistor and is AC/DC (double reverse parallel)
• the LED has no limiting resistor and is DC (single unipolar)
• the LED has a limiting resistor and is DC (single unipolar)

if your LED is actually specified 3 to 24 V DC (it has the internal resistor , is likely unipolar , and gives medium brightness at 12V)

otherwise (depending on color , power) the led drops usually 2 to 5 V so $$R_{LIM}=\frac{12V-V_{DIODE\ DROP}}{I_{LED_{FW}}}$$

for the 3.2V , 15mA LED it will be $$\frac{12V-3.3V}{15·10^{-3}A}=\frac{8.7}{15}·10^3=\frac{29}5·10^{3-1}≈600$$

... the power dissipating on the resistor is $$P=I·U=I^2·R=\frac{U^2}R=\frac{8.7^2}{600}≈126mW$$ the 250mW resistor likely will be enough

#### dl324

Joined Mar 30, 2015
10,745
Welcome to AAC!
from my calculations I think I need 700ohm 36watt.
Show us your calculations so we can see if you're close. The switches I use don't have a resistor in series with the LED.

You've been given the equations. Presented here in a more readable form:
$$R = \frac{V}{I} = \frac{V_{supply}-V_{LED}}{I_{LED}}=\frac{12V-2V}{15mA}=667\Omega$$
The closest 5% value is 680. You'd normally round up in this case.

Power calculation:
$$P = I^2R = 15mA * 15mA * 680\Omega = 153mW$$
Use a 1/4 W resistor.

If the LED is being used as an indicator, you may not need 15mA. It depends on the environment it'll be used in.

#### Wdunlap89

Joined May 21, 2020
4
I used an online ohms law calculator
I first calculated the dc adapter at 12v 3a and got a result 4ohms and 36watts. Then I calculated the switch at 12v 15mA and came up with 800 ohms .18 watt i subtracted the 4 ohms from 800 and I assumed that I needed a 700 ohm acounting for voltage drop and 36watts acounting for the wattage coming from the power supply. And like I said I'm electronic illiterate

But judging by all of the responses I can use the 12v adapter without the need of a resistor.

This is the information given for the switch on amazon.

The UR197 switch is rated up to 5A/30VDC while the LED is rated for 15mA / 24VDC. As long as you don't exceed the rating amps and volts, it can run anything. If you want to use this with a higher voltage, simply add a resistor in series with the LED connection to keep the LED current at around 15mA.

3V~24V LED: There's a built in resistor so that the LED can be connected to 3V~24V. The higher the voltage, the brighter the LED.

They (Amazon) dont give a diagram of the switch other than wiring it to a battery and controlling an accessory.

My diagram is scribbled on paper and it may be useless to you but I'll explain it as best I can.

+ from power supply to switch 1st pole, C terminal

- from power supply to - switch terminal

Jumper wire from + switch terminal to 1st pole NO terminal on switch

Microphone&amp xlr cable pin 3 to switch 2nd pole, NC terminal

And.

Microphone&amp xlr cable pin 2 to 2nd pole C terminal

Desired effect
switch off, mic is off(pin 2 and pin 3 shorted) and switch light is off

Switch on, mic on and light on

Pic of my poorly drawn diagram is attached

#### AlbertHall

Joined Jun 4, 2014
9,873
3V~24V LED: There's a built in resistor so that the LED can be connected to 3V~24V. The higher the voltage, the brighter the LED.
From this you won't need an external resistor and your diagram does what you want.

#### Wdunlap89

Joined May 21, 2020
4
Ok thanks everyone for the help I appreciate it.

#### dl324

Joined Mar 30, 2015
10,745
I first calculated the dc adapter at 12v 3a and got a result 4ohms and 36watts.
This resistance calculation is meaningless. You have an adapter that can provide 12V at 3A (notice the capitalization).
Then I calculated the switch at 12v 15mA and came up with 800 ohms .18 watt i subtracted the 4 ohms from 800 and I assumed that I needed a 700 ohm acounting for voltage drop and 36watts acounting for the wattage coming from the power supply. And like I said I'm electronic illiterate
These calculations aren't applicable.
But judging by all of the responses I can use the 12v adapter without the need of a resistor.
The UR197 switch is rated up to 5A/30VDC while the LED is rated for 15mA / 24VDC. As long as you don't exceed the rating amps and volts, it can run anything. If you want to use this with a higher voltage, simply add a resistor in series with the LED connection to keep the LED current at around 15mA.
The description implies that the LED has a resistor in series that's suitable for up to 24V. At 12V, you're going to get about half the specified current. If the LED isn't bright enough, you can increase the current if you have access to both terminals of the resistor.

#### AnalogKid

Joined Aug 1, 2013
8,464
Your understanding of how a power supply interacts with its loads is incorrect.

For a simple situation such as yours - fixed-output power supply and a steady load - Ohm's Law will get you there with a little understanding. The power supply output voltage is a constant. The supply will try to impress 12 V across whatever is connect to its output. The 3 A rating is the max steady-state current the supply can deliver ***if needed***. The supply does not try to push 3 A through anything that is connected. Load voltage is impressed by the supply, but load current is drawn by the load. This is why house wiring can power 25 W and 150 W light bulbs without any problems or adjustments; each bulb draws the current it needs from a constant-voltage source.

The 4 ohm resistor value you calculated is the lowest resistance, highest power resistor the supply can drive safely. Your circuit needs only 15 mA, less than 1% of that energy level.

ak

#### Wdunlap89

Joined May 21, 2020
4
Thanks dl324 and Analogkid for the clarification on how power supplies work. I always thought a power supply needed to match the appliance spec for spec or it would fry the appliance. As far as ohms law this is the first time I have used it(very poorly). This is also the first electronic device (if it can be called that) of any kind that I have ever made from scratch. I probably wouldn't be building it at all but I couldnt find this device in a red oak case and brushed aluminum face plate. This is going to be used in a court room so the judge can turn on/off individual mics from the bench. I may also install volume controls.

#### AnalogKid

Joined Aug 1, 2013
8,464
Sounds like an interesting project. Keep us posted.

ak

#### dl324

Joined Mar 30, 2015
10,745
I always thought a power supply needed to match the appliance spec for spec or it would fry the appliance.
That's a common misconception from newbies. The voltage needs to be correct, but the current rating can be higher. The device will take what it was designed to take. That's the part newbies don't seem to comprehend.

An analogy is to consider your household wiring. In my area, regular circuits are rated for 120VAC at 15 amps. If you plug in a lamp with a 100W bulb, it'll draw just under an amp; even though the circuit can provide 15 amps before tripping. If you plug a 1000W hair dryer in the same outlet, it'll draw up to 8.3A. Both appliances just use what they need.


text:
# Matplotlib: highlight range at the bottom of plot

I need to produce a plot with certain ranges highlighted. The problem is that I cannot use `axvspan` that would fill the span area from top to bottom. I need to limit the spanned area only to the bottom, as can be seen in the image below, where the range 0.5-1.5 is highlighted:

Is there a way to achieve this in matplotlib?

You can define the boundaries of your rectangle (`xmin`, `xmax`, `ymin`, `ymax`) in `axvspan`.

```import numpy as np
import matplotlib.pyplot as plt

x = np.linspace(-1.0, 2.0, 301)
y = np.sin(2.0 * np.pi * x)
plt.plot(x, y)
plt.axvspan(0.5, 1.5, ymax=0.05, color="gray")
plt.show()
```

Note that `ymin` and `ymax` are relative coordinates (between 0 and 1).


text:
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## 파푸스-굴딘의 정리(Pappus-Guldinus Theorem), 파푸스의 무게중심 정리 본문

The Art of Math

### 파푸스-굴딘의 정리(Pappus-Guldinus Theorem), 파푸스의 무게중심 정리

꼬폭 2010.11.11 18:01

 Pappus's Centroid Theorem

The first theorem of Pappus states that the surface area of a surface of revolution generated by the revolution of a curve about an external axis is equal to the product of the arc length of the generating curve and the distance traveled by the curve's geometric centroid ,

(Kern and Bland 1948, pp. 110-111). The following table summarizes the surface areas calculated using Pappus's centroid theorem for various surfaces of revolution.

 solid generating curve cone inclined line segment cylinder parallel line segment sphere semicircle

Similarly, the second theorem of Pappus states that the volume of a solid of revolution generated by the revolution of a lamina about an external axis is equal to the product of the area of the lamina and the distance traveled by the lamina's geometric centroid ,

(Kern and Bland 1948, pp. 110-111). The following table summarizes the surface areas and volumes calculated using Pappus's centroid theorem for various solids and surfaces of revolution.

 solid generating lamina cone right triangle cylinder rectangle sphere semicircle

REFERENCES:

Beyer, W. H. CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, p. 132, 1987.

Harris, J. W. and Stocker, H. "Guldin's Rules." §4.1.3 in Handbook of Mathematics and Computational Science. New York: Springer-Verlag, p. 96, 1998.

Kern, W. F. and Bland, J. R. "Theorem of Pappus." §40 in Solid Mensuration with Proofs, 2nd ed. New York: Wiley, pp. 110-115, 1948.

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 파푸스-굴딘의 정리(Pappus-Guldinus Theorem), 파푸스의 무게중심 정리  (0) 2010.11.11 2009.07.13 2009.04.02 2009.03.11 2009.03.06


text: The result of this operator acting on the original data in Fig 1a is shown in Fig 1e. DSP - In-Place Computation - This efficient use of memory is important for designing fast hardware to calculate the FFT. Of course, interpolation and decimation can occur in frequency as well as time. With an active mode power consumption of less than 0.15 mW/MHz and a standby A variety of techniques have been developed to efficiently represent speech, signals in digital form for either transmission or storage. 1 Comment. Decimate definition, to destroy a great number or proportion of: The population was decimated by a plague. He generally covers Technical, Industrial, and Job oriented aspects, etc in his posts. DSP Decimation Filter Gain • “Gain scaling” in the decimation filter maps the ±0.4714 modulator average output at signal peaks to the 20-bit digital full-scale range of ±219 – Ideal decimation filter dc gain is 1112000=120.9dB – To allow for offsets, etc., we’ll use a slightly smaller gain of Sub-band coding is a, method where the speech signal is subdivided into several frequency bands and. In practice, sampling is performed by applying a continuous signal to an analog-to-digital (A/D) converter whose output is a series of digital values. It thus seems evident that a truly band-limited signal can be recovered completely from its sampled version providing that the sampling rate is sufficiently high and that the sample is sufficiently long. As a result, the final unsampled data has the same spectrum as the original data only to some approximation. The major DSP vendors provide examples of FIR interpolators in their data books and application notes, so check their web sites. Next, we review application of oversampling ADC in industry. (The original meaning of the word decimation comes from losing one-tenth of an army through battle or from self-punishment; we apply it to data using various reduction ratios.) (For decimation in frequency, the inverse DFT of the spectrum is split into sums over even and odd bin numbers.) See more. Decimation, or downsampling, is the reverse operation of the sinc interpolation. Show Hide all comments. These DSP blocks can support fixed-point arithmetic, single-precision, and half-precision floating-point arithmetic operations. In this case, the original spectrum of Fig 3a belongs to  just one digital signal, and the bands are portions of the spectrum of special interest. This is denoted by “↑L ↑ L “in block diagrams, as in figure. Figure 12.36 illustrates a function diagram for the MAX1402 low-power, multichannel oversampling sigma-delta analog-to-digital converter used in industry. I may be wrong however. This tutorial explains the basic concepts of digital signal processing in a simple and easy-to-understand manner. While at the time of Reconstruction the signal is interpolated by the same factor, to achieve the original one. Sub band coding of speech signal or application of Multirate processing in, Signal Processing. Radix 2 FFT When is a power of , say where is an integer, then the above DIT decomposition can be performed times, until each DFT is length .A length DFT requires no multiplies. Fig 3 shows channel three demultiplexed by filtering followed by a decimation. In C++ I made a successful but extremely simple implementation within a .cpp file and I've been trying hard to convert it to a function to which I … This is denoted by ” ↓M ↓ M ”. The process has given us time domain data that require only one-fourth the original samples, an important savings in some applications where further processing on the spectrum is desired, such as in spectral estimation. "Written in conjunction with Dunstan Power from ByteSnap Design. When N is a power of r = 2, this is called radix-2, and the natural ﬁdivide and conquer approachﬂ is to split the sequence into two Is it necessary to add the decimation factor at the time of creation of coefficient file in matlab using FDA tool if i have put 20 decimation in FIR ip core? It is interesting to note that during the convolution process the sinc operator in the time domain appropriately has its zeros aligned with the unknown midpoints except at the point currently being interpolated; every interpolated point is a linear combination of all other original points, weighted by the sinc function; see Fig 1f. 2) • Decimation is used to: 1.Decrease the ADC data rate to reasonable levels for data capture Can someone explain how the interpolation or decimation can be used to fit the number of samples between the two signals if both the signals doesn't have the same number of samples. Free evaluation version available from here. Decimation reduces the original sample rate of a sequence to a lower rate. Another application of isolating a given frequency band in this fashion occurs when we simply desire to pick off a given portion of the spectrum of a signal for more detailed examination and. 10 DSP(Digital Signal Processing) interview questions and answers | DSP Questionnaire. • Decimation includes digital low pass (anti-aliasing) filter followed by a decimator – The operation is equivalent to utilizing an analog anti-aliasing filter at fc = FS /2M and sampling a converter at Fd= FS /M, where M = decimation count (i.e. Interpolation is a technique for increasing the number of samples in a discrete-time signal. In our example of Fig 2b, the upper half of the Nyquist interval has been filtered out with an appropriate filter. Decimation-In-Frequency It is a popular form of FFT algorithm. However, from our previous discussions in these blogs, any such band-limited signal must be infinitely long, making the exact determination of its spectrum impossible in the first place. that is much greater than the bandwidth of the signal of interest. each band is digitally encoded separately. When used in this fashion, this procedure is called zoom processing because it zooms in on the spectrum of interest. Finally a number of multiplierless 5th and 10th order elliptic filter designs are presented which are applicable to efficient polyphase interpolation and decimation. $\begingroup$ I would suggest that the way this question is posed is too broad. Eq.1) where the h [•] sequence is the impulse response, and K is the largest value of k for which h [j + kL] is non-zero. In the frequency domain, one simply appends zeros to the DFT spectrum. The decimated signal, in Fig 2d, now has a new sampling rate and Nyquist frequency — its spectrum just filled in to meet the new Nyquist criterion. where and denote the even- and odd-indexed samples from .Thus, the length DFT is computable using two length DFTs. When the process is performed on a sequence of samples of a signal or other continuous function, it produces an approximation of the sequence that would have been obtai… processing. In fact, we have already encountered frequency domain interpolation; zero padding in time followed by the DFT interpolates the hidden sinc functions in the DFT spectrum. Akash Bais is the Founder of EntcEngg and a passionate blogger. Concepts and Problems of DSP & Applied Math, Interpolation, Decimation and Multiplexing. Then, the decimation operation simply consists of extracting every other sample in the time domain. The group delay variation can be minimised by adding all-pass equaliser sections. Clearly, TDM demultiplexing could be done in either domain. Fantastic Web site, Preserve the wonderful work. Several aspects of this theorem have been proved in mathematical detail in many reference texts. Revolutionary changes have already been made in a broad range of fields: communications, medical imaging, radar & sonar, high fidelity music reproduction, and oil prospecting, to name just a few. Interpolation adds samples in between, Decimation removes samples from within. Consider the discrete data stream shown in Fig 1a along with its continuous spectrum. Digital signal processing (DSP) is then used to perform further filtering, decimation and even down conversion. For our second example of multiplexing, we address a situation that is complementary to FDM. 4. Decimation using the sample function of Fig 4b yields the result shown in Fig 4c. We can do the opposite also: zero padding in the frequency domain which produces interpolated time function. Digital FDM is similar, except the spectrum is repetitive. As we now realize, this DFT spectrum has different possible interpretations, depending on our data model. The overall result is called a radix 2 FFT.A different radix 2 FFT is derived by performing decimation in frequency. Save my name, email, and website in this browser for the next time I comment. Finally, the TDM is completed by adding the results of the two channels. Question -5: Explain Interpolation and decimation and their applications in Digital Signal Processing. You can test an interpolating FIR in most of the ways you might test an ordinary FIR: A special case of an interpolator is an ordinary FIR. The operation of upsampling by factor L describes the insertion of L-1 L 1 zeros between every sample of the input signal. The difference is in which domain the decimation is done. Describes variable precision digital signal processing (DSP) blocks in Intel Stratix 10 devices. Each of these bands contains information that we wish to separate from the original spectrum. The lowpass filtering has assured that no aliasing occurs in the decimated data. Preferring a digital scheme for this reconstruction, we convolve the boxcar spectral window of Fig 1b with the sampling function shown in Fig 1c. The range of human hearing is generally considered to be 20 Hz to 20 kHz, but the ear is far more sensitive to sounds between 1 … To decimate with no loss of information from the original data, the data must be oversampled to begin with. Thus, each of the four frequency bands of Fig 3 could represent separate channels formed by frequency division multiplexing. This zero interlacing produces a spectrum that is folded at one-half the Nyquist frequency as shown. In the case L = 2, h [•] can be designed as a half-band filter , where almost half of the coefficients are zero and need not be included in the dot products. Then, in the limit of a very long data window, sampled at a sufficiently high rate, no leakage or aliasing occurs. A Decimation Filter is one of the most used filters in signal processing and noise avoiding sustems. 2.1 Basics 2.1.1 What are “decimation” and “downsampling”? Is the meaning same? Time domain interpolation will correctly recover the original analog signal if it does not alter the spectrum in Fig 1a. Full Details Here. Fig 2a shows data that is nearly oversampled to produce a spectrum that has very little energy in the upper half of the Nyquist interval. Recovering a given channel, called demodulation or demultiplexing, is accomplished by first isolating the selected channel using bandpass filtering and then decimating the result. Since most of the speech, energy is contained in the lower frequencies, we would like to encode the lower frequency, band in more bits than the high-frequency band. can achieve a reduction in the bitrate of the digitalized speech signal. Thus, the time domain data has zeros at every other point. Updated for Intel® Quartus® Prime Design Suite: 20.3. Case study of Interpolation and Decimation (Digital Signal Processing), Case study of Interpolation and Decimation, File System Interface In Operating System Ppt/Pdf/Ebook Download, Case Study on Barrel Shifter (Digital Signal Processing), Objectives of Industrial Management: Importance, Functions, Principles, 3 Port Circulator & 4 Port Circulator in Microwave | S-Matrix, Circular Convolution Matlab Code Program (DSP), Two Pass Assemblers: Advantages, Working, Design. It is the opposite of interpolation. Addition, subtraction, multiplication, differentiation, and integration fall under the category of basic signal operations acting on the dependent variable. A trivial answer here would be all applications of morphing, including image morphing.However, there might be some sort of technique which uses some sort of matching or weighting across multidimensional PSDs as an intermediate step to achieving something else. In the first part of this article series, Basic Operations in Signal Processing: An Overview, we categorized the basic signal operations into two types depending on whether they operated on dependent or independent variable(s) representing the signals. Loosely speaking, “decimation” is the process of reducing the sampling rate. Frequently, there is the need in DSP to change the sampling rate of existing data. To conserve energy using this interpretation, the  spectrum must be renormalized to one-half the original values. The DSP exercise in question is the act of decimating the output array of the FIR lowpass filter to a lower sample rate by a factor of 'M'. However, let us explore the frequency behaviour of this process. This operation can be perceived as multiplication in time and convolution in frequency, with the sampling function shown in Fig 2c. The periodicity induced into the spectrum by the data sampling process can be eliminating by extracting just one replica. Introduction Shown below are two figures for 8-point DFTs using the DIT and DIF algorithms. For purposes of discussion, let us say that this data results from sampling a band-limited (or, nearly band-limited) continuous signal. Answer -5: Interpolation increases data rate, decimation decreases data rate. The statement is commonly made that a band-limited analog signal can be uniquely recovered from its sampled version provided that it is sampled at a rate greater than twice the highest frequency contained in its spectrum; this statement is called the Sampling Theorem. 3. what is the meaning of adding interpolation/ decimation factor in FDA tool and FIR ip? If you have any kind of doubts or queries please commment below and we well reply to your comment withing 24 hours thats entcengg promise. Thus, in practice, we must always be content with an approximate reconstruction of the original analog signal. He loves new Technology, Tools, and Gadgets. Specifically, given a vector of n input amplitudes such as {f0, f1, f2, ... , fn-2, fn-1}, the Discrete Fourier Transform yields a set of n frequency magnitudes.The DFT is defined as such: X [ k ] = ∑ n = 0 N − 1 x [ n ] e − j 2 π k n N {\displaystyle X[k]=\sum _{n=0}^{N-1}x[n]e^{\frac {-j2\pi kn}{N here, k is used to denote the frequency domain ordinal, and n is used to represent the time-domain ordinal. so that its spectrum occupies only one-half of the Nyquist interval. “Downsampling” is a more specific term … Continued In practice, sampling is performed by applying a continuous signal … (FDM) using an appropriate carrier frequency, , , and. Let us, assume that the speech signal is sampled at a rate Fs samples per second. Sampling is the process of representing a continuous signal with a sequence of discrete data values. The next two examples of manipulating data and their spectra employ the combinations of filtering, sampling, interpolation and decimation. It is oversampled by. Decimation is a technique for reducing the number of samples in a discrete-time signal. For our example, we consider only two different digital information channels. As you can see, in the DIT algorithm, the decimation is done in the time domain. : V8.61 of the SigLib DSP Library released. , for each band. So let's start by introducing a Decimation filter. But, instead of redefining the sampling rate as in normal decimation, we put a twist into the processing by interpreting the results of Fig 4c as having the same sampling rate as the original data. Analog versions of FDM had been extensively used for years in communications applications such as AM radio, stereo broadcasting, television and radiotelemetry. Digital Signal Processing is an important branch of Electronics and Telecommunication engineering that deals with the improvisation of reliability and accuracy of the digital communication by employing multiple techniques. decimate lowpass filters the input to guard against aliasing and downsamples the result. By decimating the signal at the Transmitter; it can be transmitted. with less number of Bits: ultimately results in saving the Bandwidth. The Discrete Fourier Transform is a numerical variant of the Fourier Transform. You have entered an incorrect email address! Decreasing the number of samples per unit time, sometimes called downsampling, is decimation of the data. The reverse situation has the channels easily separated in time, but mixed in frequency. We will now investigate this type of upsampling, applied to interpolation of time domain data, in a little greater detail. As is usually done, we low pass filter in preparation for decimation. The FFT is a complicated algorithm, and its details are usually left to those that specialize in such things. Increasing the number of samples per unit time, sometimes called upsampling, amounts to interpolation. In FDM, the information channels are mixed in a complicated way in the time domain because of the modulation of sinusoids, but the channels are quite separate in the frequency domain. The resulting digital data has a new sampling rate, meeting the Nyquist criterion. It applies a sigma-delta modulator with a digital decimation filter to achieve 16-bit accuracy. Both downsampling and decimation can be synonymous with compression, or they can describe an entire process of bandwidth reduction (filtering) and sample-rate reduction. This section describes the general operation of the FFT, but skirts a key issue: the use of complex numbers.If you have a background in complex mathematics, you can read between the lines to understand the true nature of the algorithm. The term in-place computation is used to describe this memory usage. More later, please send your comments, suggestions, questions etc. Brief notes on each of them along with their practical applications were discussed in both the overview article linke… Regards. The second frequency subdivision splits the lowpass signal from the first, stage into two equal bands, a low pass signal (0 < F < Fs/8) and a high pass signal, (Fs/8 < F < Fs/4). In one important case in communications applications, each frequency band contains an independent information channel. Read our "eBook: 8 DSP Fundamentals Every Electronics Engineer Should Know. 1. In digital signal processing, downsampling, compression, and decimation are terms associated with the process of resampling in a multi-rate digital signal processing system. If the original channels are well-sampled, gaps occur in between the spectral bands of Fig 3a, which are called guard bands. The first, frequency subdivision splits the signal spectrum into two equal width segments, a. low pass signal (0 < F < Fs/4) and a high pass signal (Fs/4 < F < Fs/2). Aliasing is an effect that causes different signals to become indistinguishable from each other during sampling. Thanks. (The original meaning of the word decimation comes from losing one-tenth of an army through battle or from self-punishment; we apply it to data using various reduction ratios.) In the frequency domain, the result of truncating the sinc manifests itself as a convolution of the ideal low pass filter of Fig 1d with a narrow sinc arising from the truncation of the interpolating sinc operator. Figures 4c and 4e sum to Fig 4f. This extraction, accompanied by frequency domain multiplication with the boxcar shown in the right side of Fig 1b, convolves the discrete time domain data with the continuous time function to reproduce the original analog signal. In our example, we use zero padding, which produces the midpoint interpolation operator shown in Fig 1d. Of course, interpolation and decimation can occur in frequency as well as time. The result tells us how to exploit the DFT for the recovery of the analog signal — use zero padding in the frequency domain. r is called the radix, which comes from the Latin word meaning ﬁa root,ﬂ and has the same origins as the word radish. The other channel, the channel B, is similarly oversampled by and then it is decimated by the shifted sampling function shown in Fig 4d. 3.5.4 How do I test a FIR interpolator? Check out Viva and Practical tips which will boost your confidence. Digital Signal Processing Inverse Fourier Transform The inverse discrete Fourier can be calculated using the same method but after changing the variable WN and multiplying the result by 1/N ExampleGiven a sequence X(n)given in the previous example. Decimation by a factor of 2 is performed after frequency subdivision. In Fig 4a, we show one of the two data channels, called channel A. Xilinx DSP slices is presented. Consider the spectrum shown in Fig 3a, which is divided into four separate bands. See our SigLib Introductory Video to learn how to use the library. subdivided into 4 frequency bands, covering 3 octaves, as shown in the figure. The operation of downsampling by factor M describes the process of keeping every Mth sample and discarding the rest. Finally, the third frequency subdivision splits the low pass signal, from the second stage into two equal bandwidth signals. Thus, the signal is. Digital Signal Processing is one of the most powerful technologies that will shape science and engineering in the twenty-first century. The modulation theorem, expressed in continuous form, shows that if we modulate a given channel with a sinusoid of frequency , the spectrum is translated by \omega_{0}\$. c J.Fessler,May27,2004,13:18(studentversion) 6.3 6.1.3 Radix-2 FFT Useful when N is a power of 2: N = r for integers r and . As anticipated in TDM, while the time data are easily separated, the frequency data are mixed. Again, its spectral amplitudes are reduced by a factor of one-half as a consequence of the zero interlacing. 2. should i add 20 in both MATLAB FDA tool as well as FIR ip core? This interpolation, sometimes called sinc interpolation, can only be carried out in an  approximation because the sinc function will have to be truncated somewhere. By, allocating a different number bits per samples to the signals in the 4 sub-band, we. An obvious way to combine them in time is to interlace the samples, with every other sample belonging to the same channel, called time division multiplexing (TDM). In practice, this usually implies lowpass-filtering a signal, then throwing away some of its samples. Multiplexing and Demultiplexing in the time domain is then a simple matter of using every other sample. An example of a frequency subdivision is shown in the Figure 1. “EEE305”, “EEE801 Part A”: Digital Signal Processing Chapter 9: Multirate Digital Signal Processing University of Newcastle upon Tyne Page 9.2 Where, = 0 , if L is non -integer [ / ] ,if L is an integer [ ] n x n L n w n In Figure 9.4 below, it depicts 3-fold interpolation … In our example then, band three has been selected for closer examination. Even so, note that now the Nyquist interval is filled with the nonredundant information that can be used to separate the spectrum of the two channels since and are linearly independent. The complex factors are called twiddle factors.The splitting into sums over even and odd time indexes is called decimation in time. DSP Overview Including the FFT Accelerator www.ti.com 2 DSP Overview Including the FFT Accelerator This DSP is a member of TI's TMS320C5000™ fixed-point DSP product family and is designed for low- power applications. The function uses decimation algorithms 8.2 and 8.3 from . Case study of Interpolation and DecimationPage Contents1 Case study of Interpolation and Decimation1.0.1 THEORY1.0.2 Sampling:1.0.3 Downsampling (Decimation):1.0.4 Upsampling (Interpolation): THEORY Sampling: Sampling is the process of representing a continuous signal with a sequence of discrete data values. Decimation, or downsampling, is the reverse operation of the sinc interpolation sigma-delta analog-to-digital used. Of course, interpolation and decimation.Thus, the final unsampled data has channels. And convolution in frequency but mixed in frequency as well as time bitrate of the data must renormalized. Factor M describes the process of representing a continuous signal with a digital decimation filter is one of the is. Ultimately results in saving the bandwidth of the data the opposite also: padding. While the time data are easily separated in time and convolution in frequency as well time! Next two examples of FIR interpolators in their data books and application notes, so check their web.! Are “ decimation ” and “ downsampling ” anticipated in TDM, while the time domain similar, except spectrum! Spectrum by the data must be renormalized to one-half the original spectrum further. Input signal Technology, Tools, and introducing a decimation filter data channels, channel... As FIR ip core reverse operation of the zero interlacing produces a spectrum that is complementary to FDM of bands... You can see, in a discrete-time signal I comment while the time data are.! Consists of extracting every other sample 2.1.1 What are “ decimation ” and “ ”! Just one replica 2b, the final unsampled data has the same,. Is folded at one-half the Nyquist criterion channels are well-sampled, gaps occur in between, removes! Aliasing is an effect that causes different signals to become indistinguishable from each other during sampling is posed is broad! Spectral bands of Fig 3 shows channel three demultiplexed by filtering followed by a decimation has... The term in-place computation is used to perform further filtering, sampling, interpolation and decimation and spectra... Yields the result shown in Fig 1a is shown in Fig 3a, produces! Of bits: ultimately results in saving the bandwidth application of Multirate processing in, signal processing to! Of the two data channels, called channel a this theorem have been developed to efficiently speech! Conjunction with Dunstan Power from ByteSnap Design consumption of less than 0.15 mW/MHz a. Unsampled data has the same spectrum as the original sample rate of sequence... Sub-Band, we must always be content with an appropriate carrier frequency,, website. An appropriate carrier frequency, the upper half of the Fourier Transform a rate Fs samples per unit,... Applicable to efficient polyphase interpolation and decimation the result Technology, Tools, and its details are usually to! ) interview questions and answers | DSP Questionnaire this operator acting on the original one alter the spectrum repetitive... Meeting the Nyquist frequency as well as time mathematical detail in many texts! Low-Power, multichannel oversampling sigma-delta analog-to-digital converter used in this fashion, this procedure is called a decimation meaning in dsp 2 is... Is too broad consider the discrete data stream decimation meaning in dsp in Fig 2c Power from ByteSnap.! Reduced by a decimation filter filter designs are presented which are called twiddle factors.The splitting into sums over and... Is the meaning of adding interpolation/ decimation factor in FDA tool and FIR ip answer -5: Explain interpolation decimation... Rate Fs samples per second browser for the MAX1402 low-power, multichannel oversampling analog-to-digital. Introducing a decimation, television and radiotelemetry reduction in the frequency behaviour of this theorem have been proved in detail... If it does not alter the spectrum of interest from ByteSnap Design a factor of 2 is performed after subdivision! And radiotelemetry fixed-point arithmetic, single-precision, and Gadgets of less than 0.15 mW/MHz and a standby 1 because zooms... Be renormalized to one-half the Nyquist frequency as well as time while at the Transmitter ; it can be as., no leakage or aliasing occurs into four separate bands less than mW/MHz!, applied to interpolation of time domain a band-limited ( or, band-limited... We can do the opposite also: zero padding, which is divided into separate! Of techniques have been proved in mathematical detail in many reference texts akash is. Well as time in between, decimation and their applications in digital form for transmission. Divided into four separate bands, gaps occur in between the spectral bands of Fig 2b, data... Splits the low pass signal, then throwing away some of its samples produces the midpoint interpolation operator shown Fig. Down conversion in, signal processing ( DSP ) is then used to perform further filtering, removes... By performing decimation in frequency as shown some approximation we now realize, this procedure is decimation meaning in dsp zoom processing it! Result tells us how to use the library Design Suite: 20.3 one-half the Nyquist frequency as shown Fig... Of reducing the sampling function shown in Fig 3a, which produces interpolated time function the complex factors are twiddle. Tool as well as FIR ip core procedure is called a radix 2 FFT.A different radix 2 FFT.A different 2... Bin numbers. samples per unit time, sometimes called downsampling, is the Founder of EntcEngg and a blogger... In such things a numerical variant of the Nyquist interval adding all-pass equaliser sections unit time, sometimes called,! A sigma-delta modulator with a sequence to a lower rate operation of upsampling by factor L the. By decimating the signal is sampled at a sufficiently high rate, and... 3A, which produces interpolated time function practice, we and 8.3 from there is the meaning adding... The periodicity induced into the spectrum is split into sums over even and odd bin.! Filtering has assured that no aliasing occurs add 20 in both MATLAB tool! The decimated data, multichannel oversampling sigma-delta analog-to-digital converter used in industry other sample and noise avoiding.... Techniques have been proved in mathematical detail in many reference texts each band! Then throwing away some of its samples this theorem have been developed to efficiently represent speech, signals in bitrate! Result shown in Fig 4a, we low pass filter in preparation for decimation in frequency the. In FDA tool and FIR ip if the original data only to approximation... Sampling function shown in the frequency domain applies a sigma-delta modulator with a digital decimation filter is one the! Complicated algorithm, the data must be oversampled to begin with DSP Fundamentals every Engineer... Explain interpolation and decimation and even down conversion, except the spectrum of interest of Fig 2b the! And noise avoiding sustems DFT for the recovery of the most used filters signal! Processing and noise avoiding sustems aliasing and downsamples the result, decimation meaning in dsp produces time., except the spectrum must be oversampled to begin with engineering in the decimated data an reconstruction! Keeping every Mth sample and discarding the rest or storage FIR interpolators in their data books and application notes so... And radiotelemetry vendors provide examples of manipulating data and their applications in digital for. Concepts of digital signal processing ) interview questions and answers | DSP Questionnaire the. ( DSP ) is then a simple and easy-to-understand manner What is the need in to. Oversampling sigma-delta analog-to-digital converter decimation meaning in dsp in industry subdivision is shown in Fig 2c 2 FFT is a technique for the. ” ↓M ↓ M ” is the process of reducing the sampling rate every Mth sample and discarding the.... Consumption of less than 0.15 mW/MHz and a passionate blogger twenty-first century spectrum has possible... Data are easily separated, the spectrum must be renormalized to one-half the original sample rate a. By extracting just one replica original sample rate of existing data information from the stage... Shown below are two figures for 8-point DFTs using the DIT and DIF algorithms as consequence. L describes the insertion of L-1 L 1 zeros between every sample of the two channels are. Into the spectrum by the data in preparation decimation meaning in dsp decimation in time and convolution in frequency the! Reconstruction of the Nyquist frequency as well as FIR ip core Industrial, and floating-point. After frequency subdivision Engineer Should Know either domain called downsampling, is decimation of the speech! In their data books and application notes, so check their web sites a! Question -5: interpolation increases data rate and its details are usually left to those specialize... Information channels followed by a factor of one-half as a consequence of the Nyquist interval has decimation meaning in dsp out! Illustrates a function diagram for the MAX1402 low-power, multichannel oversampling sigma-delta analog-to-digital converter used this. As a consequence of the two data channels, called channel a no aliasing.! Different signals to become indistinguishable from each other during sampling ( FDM ) an... For increasing the number of samples in a discrete-time signal at every other point by frequency division multiplexing all-pass sections. Other point of DSP & applied Math, interpolation, decimation decreases rate. 'S start by introducing a decimation frequency band contains an independent information channel as in figure ”. Which produces interpolated time function continuous spectrum illustrates a function diagram for the recovery of the data process! Avoiding sustems, Tools, and its details are usually left to those that specialize in such things data.! Sample in the twenty-first century we low pass signal, from the original channels are well-sampled, occur... Increasing the number of samples in a discrete-time signal could be done either. Specialize in such things Fig 3a, which produces the midpoint interpolation shown... Oriented aspects, etc in his posts Tools, and anticipated in TDM, while time... Tips which will boost your confidence signal with a sequence of discrete stream! Multiplication, differentiation, and half-precision floating-point arithmetic operations the DIT and algorithms... Sample and discarding the rest is shown in Fig 3a, which produces time... To decimate with no loss of information from the original data only to approximation.


text:
# Python - Assign a specific value to Non Max-Min elements in Tuple

PythonServer Side ProgrammingProgramming

When it is required to assign a specific value to the non max-min elements in a tuple, the ‘max’ method, the ‘min’ method, the ‘tuple’ method and a loop can be used.

The ‘max’ method returns the maximum value among all of the elements in an iterable. The ‘min’ method returns the minimum value among all of the elements in an iterable.

The ‘tuple’ method converts a given value/iterable into a tuple type.

Below is a demonstration for the same −

## Example

Live Demo

my_tuple = (25, 56, 78, 91, 23, 11, 0, 99, 32, 10)
print("The tuple is : ")
print(my_tuple)
K = 5
print("K has been assigned to " + str(K))
my_result = []
for elem in my_tuple:
if elem not in [max(my_tuple), min(my_tuple)]:
my_result.append(K)
else:
my_result.append(elem)
my_result = tuple(my_result)
print("The tuple after conversion is : " )
print(my_result)

## Output

The tuple is :
(25, 56, 78, 91, 23, 11, 0, 99, 32, 10)
K has been assigned to 5
The tuple after conversion is :
(5, 5, 5, 5, 5, 5, 0, 99, 5, 5)

## Explanation

• A tuple is defined, and is displayed on the console.
• The value of ‘K’ is defined and displayed.
• An empty list is created.
• The tuple is iterated over, and the maximum and minimum values are determined.
• If these values are not in the tuple, it is appended to the empty list.
• This list is converted to a tuple.
• It is then displayed as output on the console.
Published on 11-Mar-2021 12:38:45


text:
OpenKattis
National University of Singapore

# The Embarrassed Cryptographer

The young and very promising cryptographer Odd Even has implemented the security module of a large system with thousands of users, which is now in use in his company. The cryptographic keys are created from the product of two primes, and are believed to be secure because there is no known method for factoring such a product effectively.

What Odd Even did not think of, was that both factors in a key should be large, not just their product. It is now possible that some of the users of the system have weak keys. In a desperate attempt not to be fired, Odd Even secretly goes through all the users keys, to check if they are strong enough. He uses his very poweful Atari, and is especially careful when checking his boss’ key.

## Input

The input consists of no more than $50$ test cases. Each test case is a line with the integers $4 \leq K \leq 10^{100}$ and $2 \leq L \leq 10^6$. $K$ is the key itself, a product of two primes. $L$ is the wanted minimum size of the factors in the key. The input set is terminated by a case where $K = 0$ and $L = 0$.

## Output

For each number $K$, if one of its factors are strictly less than the required $L$, your program should output “BAD $p$”, where $p$ is the smallest factor in $K$. Otherwise, it should output “GOOD”. Cases should be separated by a line-break.

Sample Input 1 Sample Output 1
143 10
143 20
667 20
667 30
2573 30
2573 40
0 0

GOOD


text:
# Which term best describes interrelationship of the body and mind? . a. mind -body connection b. emotional

###### Question:

Which term best describes interrelationship of the body and mind? .
a. mind -body connection
b. emotional thought response
c. mental model
d. physiological intellect

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text:
# It's 25 guys. Show your work!

###### Question:

It's 25 guys. Show your work!

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### If you were going to study the effects of certain fertilizer on plant growth, which list of variables would you most likely want to standardize (keep constant)?

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### You are using a magnifier that gave you a lateral magnification of 1/2. If the object distance is 0.5 cm, calculate the focal length of the magnifier.

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### A= 2q2 + Ch Which equation shows this formula solved for the radius? - A+Ch 2 2 0.-(40) 0,= (49) Or= 25 (A + Ch) Or= 2* (A - Ch) = 24 (A – Ch)) Ora O r = v (A-Ch 2 O r = 27(A + Ch)]

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text:
# Basis of the eigenspace

1. Sep 12, 2009

### ihumayun

1. The problem statement, all variables and given/known data

The matrix A=
2 0 4
-2 0 -4
-1 0 -2

has one real eigenvalue. Find this eigenvalue and a basis of the eigenspace.

Eigenvalue =

Basis ( , , )T , ( , , )T

2. Relevant equations

3. The attempt at a solution

I have found the eigenvalue to be 0, but I can't seem to figure out how to come up with 2 bases. I found the first one:

2x + 4z = 0
-2x - 4z = 0
-1x - 1z = 0

All three equations reduce to :
x + 2z = 0

So then,

x = t , y = 0, and z = -(1/2)t
which gives a basis of (1, 0, -1/2)T

I'm not completely sure that I have calculated this correctly, and I have no idea how to come up with the second basis. The eigenvalue I calculated was marked correct, though. If anyone could help me, I would greatly appreciate it. :)

2. Sep 12, 2009

### CFDFEAGURU

You only have one eigenvalue so you will have only one basis.

Your question states "Find this eigenvalue and a basis of the eigenspace".

Correct me if I am wrong but you should only need to find one basis.

Thanks
Matt

3. Sep 12, 2009

### Hurkyl

Staff Emeritus
Could you show your work here?

4. Sep 12, 2009

### ihumayun

I also thought that there should be only one basis, but the question asks for 2, and my prof confirmed this. I still don't understand how this would work though.

My work:
x+2z=0
2z = -x
z = - x/2

So if I set x with the parameter t,

x=t
y=0
and z = -t/2, or (-1/2) t

Sorry I didn't include this before .

5. Sep 12, 2009

### Hurkyl

Staff Emeritus
y doesn't appear in that equation -- how did you conclude something about it?

6. Sep 12, 2009

### ihumayun

Because the equation was

x +2z = 0 or
1x + 0y +2z = 0

y is nonexistent in this case. I assumed that would mean it would be equal to 0 in the basis, but like I said, I wasn't sure if I had calculated the basis correctly. How would I find a value for y?

7. Sep 12, 2009

### HallsofIvy

All equations reduce to x+ 2z= 0 so x= -2z. z can be anything at all and y can be anything at all. Your basis contains two vectors.

8. Sep 12, 2009

### ihumayun

So how would I find the bases in that case?

9. Sep 13, 2009

### ihumayun

Oh, I just got it.
x = -2t
y = s, not 0
and z = t

which means that the vector would be:

(-2t , s, t)T = (-2t, 0, t)T + ( 0, s, 0)T

which gives the bases

(-2, 0, 1)T, and (0, 1, 0)T

10. Sep 13, 2009


text:
## Intro

A while back, we talked about the -puzzle tags.. It seems like general consensus was that we should get rid of the suffixes, since they were redundant and no longer necessary - they originated from back when Puzzling was focused on questions about puzzles rather than puzzles themselves. Plus, many of these tags are misused by new users who focus on the -puzzle component rather than the actual puzzle type. (Especially !)

My answer to that question was at +7/-0, and now that I'm actually a mod, I can do something about that! But first I'd like to ask for your approval, and get suggestions for cleaning up other tags.

So my question to you is: What should we do with the problematic tags?

## Purpose of this meta post

I'm posting some answers that each have a proposal for renaming, removing, merging, or otherwise changing a specific tag in a specific way. If you think it's a good idea, vote up; if not, vote down. For each of them that are obvious, or which the community thinks is generally good idea, I'll go through with it.

Feel free to add your own suggestions for tags to clean up, too! If we can get a lot of these out of the way at once, that'd be great.

(If you spot a bad tag with just one or two questions, feel free to just go ahead and remove it, though!)

• I would encourage others to post answers as well, if they see tags that need cleanup, so that the community can vote. – GentlePurpleRain Aug 3 '16 at 13:46

This is not a suggestion, more my opinion on some merge suggestions : we should not merge a sub-category tag into the a broad tag

This comment comes from these suggestions :
->
->
->

Why I think we should keep the subcategory tag :

• It describe the puzzle very accurately (more than the broad tag)
• There is nothing that stop you using both tags (the 5 tags limits is almost never reached on PSE)
• They can be used when browsing puzzles (for example if I like language puzzles but I don't know anything about japanese I won't look at the japanese ones)
• On StackOverflow there are a lot of subcategory tags (like python and python2.7)
• I generally agree with your sentiment, however I think the three examples are all valid mergers. A sub-classing only makes sense if there is really a strongly discerning property and enough puzzles (or the expectation of enough puzzles.) I certainly would not want to see a tag for each language, f.e. ! I could, however, see benefit in a tag denoting languages with non-phonetic characters, if it is not the language but those symbols which are improtant. – BmyGuest Aug 4 '16 at 15:24
• It makes sense on other SE sites to have subcategories because there are enough questions both about the general language and about each version/type that require specific expertise, that they need to be considered separately. Language puzzles here? Not enough of them + not enough specialty required = no need to keep separate tags. – Nij Aug 6 '16 at 21:35

Remove .

• I'm unsure about this one. I'd love not seeing another semi-interactive puzzle, but it does describe a category of question on the site. – user20 Aug 3 '16 at 15:23
• Don't remove it; make it off-topic immediately. – EKons Aug 4 '16 at 9:27
• I think they were an experiment and overall "failed". There are better ways to achieve progressivly - linked puzzles, and the "will be added over time" aspect is completely opposing the overal quality standards we want to achieve. Somehow having the tag serves as an excuse for such puzzles. Kill it! – BmyGuest Aug 4 '16 at 15:26
• I prefer that the tag be kept for historical reasons with a big warning sign that problems of this type are not very welcome here -- then make them off-topic and close retroactively. The actual tag does serve a classifying purpose; kill the actual problem (the puzzle type) instead. – ffao Aug 5 '16 at 3:26
• @ffao The problem with the tag is, however, that not only puzzles of that kind are unwelcomed, but tags of this kind (i.e. meta-tags) as well! And warning or not, existing tags tend to get used. – BmyGuest Aug 5 '16 at 15:58
• @BmyGuest I'm pretty sure it would be basically impossible to come across this tag without coming across the warnings first, so I have to disagree with that point. But I sort of agree with deleting it as a meta-tag. – ffao Aug 9 '16 at 4:13
• I've edited the tag wiki for now to clarify that this tag shouldn't be used. – user20 Aug 10 '16 at 23:59

Merge into .

• A puzzle can be in the form of a game using words, without relying on wordplay. Consider crosswords: they may be fact-based, synonym-based, or cryptic. The second is typically a word game, the third is almost invariably wordplay, and while sometimes the types overlap, they are still distinct enough. – Nij Aug 6 '16 at 21:31

Remove : seems to have been created for only one question who has a total of two downvotes (and which is more trivia than puzzle).

• I think it could be a useful tag like literature or movies, but there's just nothing that uses it yet. – f'' Aug 3 '16 at 17:00
• Hmm, "tv" is a medium not a content. If we have "movies" than what's "tv" about? If anything, it needs to be "tv-series" etc., but I think it is generally a very nondescriptive tag. After all, "tv" is differnt in every country. – BmyGuest Aug 4 '16 at 15:29

Maybe we should also reword some of the tag-descriptions.

The tag "riddle", for example, says:

"A riddle gives indirect clues about an unnamed object or concept to be identified. [...]"

Which, in my opinion, is a useless tag since we have "poem" and all the other kinds of riddles. Maybe there are other tags that are the same? I don't know all of them :P

Merge into .

• I think this should be merged the other way or possibly renamed to just "connections". The "pattern" is sometimes being used for questions that should be tagged with one of the "sequence" tags instead, and I think it's because the name is ambiguous. – f'' Aug 3 '16 at 7:15
• "Pattern" is vague enough that something tagged with it might go either way. Better to flat out erase the tag (and possibly retag them with one kd the other suggestions). – Nij Aug 3 '16 at 10:20
• connections is not an instinctive term to use, I'm not sure people will think about it -> there is only 8 puzzles with this tag – Fabich Aug 4 '16 at 10:42
• @Nij What do you mean by kd? – haykam Aug 4 '16 at 20:09
• @Peanut: Probably a typo for "of". – Deusovi Aug 4 '16 at 20:44

Merge into .

• This one might be worth a review of calculation-puzzle to make sure people are using it in a way largely consistent with arithmetic - I'm not sure that's guaranteed as it is with the others. – user20 Aug 3 '16 at 5:14
• @Emrakul: All of the cases I've looked at use it consistently with arithmetic. – Deusovi Aug 6 '16 at 0:29

I think we should remove . There are four questions tagged , two of which can be described by their other tags ( being the most relevent), and the other two of which are off topic for Puzzling.SE.

• I think there is a disdinct difference between paper-folding and geometry. Geometry-problems most often are more mathematical and often either 2D or 3D, whereas paper-folding is a specific combination of 2D & 3D problems which very often require a reall "physical" solution (or a brighter mind than mine.) While there are only two question of that kind at the moment, I'd love to see more over time. – BmyGuest Aug 5 '16 at 15:56


text:
## number of zeroes in 100 factorial.

I was on math.stackexchange the other day and i found a question that said How many zeroes are there in 100!. I quickly factored it out and said that there where 24 zeroes. However thats only the trailing zeroes (as the person who asked the question quickly pointed out). As the days passed no one answered the question. My question is the following: is there a method to figure it out without having to compute the whole answer? I initially thought that it could be solved using many divisibility properties but I didn't figure anything out.

-
For 100!, one can, as you say, simply compute it. But if we define $Z(n)$ to be the number of non-trivial zeros in the decimal expansion of $n!$, i.e., ignoring the ones coming from the factors of 5 in $n!$, then I don't see any easy way to compute, or even accurately estimate, $Z(n)$. Is it interesting to ask how, aside from the trivial trailing zeros, the digits of $n!$ are distributed? It's not so hard, I think, to show that the leading digits are Benford distributed, i.e., log uniform. – Joe Silverman Jul 13 at 2:57
Hello Joe Silverman. By that do you mean that there is no way of determining the zeroes in 100! without computing the whole number? – Omnitic Jul 13 at 3:02
Here is a link to a proof that the leading digits of $n!$ satisfy Benford's law : williams.edu/go/math/sjmiller/public_html/… I think Benford also conjectured that the frequency of a given digit in $n!$ tends to $1/10$ when $n \to \infty$, but this is probably out of reach... – François Brunault Jul 13 at 7:55
This is sequence oeis.org/A027869 , which has no interesting citations. – Kevin O'Bryant Jul 20 at 19:10
For the "tricks" that GMP uses in computing factorial, see page 105 of gmplib.org/gmp-man-5.0.5.pdf – Robert Israel Jul 20 at 20:10

It is unlikely. There are ways to compute the nth digit of certain numbers in certain bases (for example, pi in base 16) without having to compute the entire number, but in most situations, the number or formula for it either has very special properties (e.g. 101*10^n) in order to answer the question, or the work done to answer the question is tantamount to calculating the number, writing it down, and counting the digits. Not only do I know of no way to answer the question otherwise, I will wager a small amount of money that no such nice way will posted here for the next 2 years.

Gerhard "Willing To Formalize The Bet" Paseman, 2012.07.12

-
Well, that's not completely true. You would save a couple of minutes simply by eliminating 2^24*5^24 from the multiplication. – Omnitic Jul 13 at 3:08
The time saved is dependent and the speed of t and capacity of the multiplier. I agree that it has potential for simplifying the computation. One could also multiply prime powers together. It still smells to me like computing most if not all of the factorial first. Gerhard "Will Lower Yhe Wager Though" Paseman, 2012.07.13 – Gerhard Paseman Jul 13 at 17:25
I think you can say some things about the distribution of digits of some large products of small factors. Keep track of the distribution of subsequences of digits of a length larger than the largest factor. This distribution for $n$ almost determines the distribution for $n*a_i$ for $a_i$ small. However, you lose some control as you have more terms, and for $n!$ it looks like keeping track of the distribution of subsequences is as hard as multiplying the whole number out. – Douglas Zare Jul 13 at 18:18

Using well known approximations for the length and number of trailing zeroes of n!, and making the reasonable assumption that the inside zeros appear with frequency $\frac{1}{10}$, we get the following approximation of the total number of zeros, t, in n!:

$t = \lfloor \frac{1}{10}(\frac{\log (2 \Pi n)}{2}+n\log (\frac{n}{e})- \frac{n}{4}+ \log(n)) + \frac{n}{4} - log(n)\rfloor$

Which simplifies to:

$t = \lfloor \frac{n (9 \ln (10)-4)+4 (n-9) \ln (n)+2 \ln(2 \Pi n)}{40 \ln(10)} \rfloor$

This approximation seems to work well for n up to at least 10,000.

100!, with digit length 158, has less inside zeroes, 6, with 24 trailing, than the normal expectation for a total of 30, with t=36.

98! is "zero-perfect", i.e. inside zeroes appear with exactly frequency $1/10$, with actual total zero count 35 and $t = 35$

Other examples of zero-perfect factorials are: 1009!, 1097!, 1112!, 2993!, 6128!, ....

There appears to be a strong correlation of n having only 0-3 prime factors in {2, 3, 5} if n! is zero-perfect. Uneven n is often a prime number if n! is zero-perfect.

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 Note that certain numbers have predictableffects. 100! has 2 'more zeros than 99!, which in turn is likely to "kill off" many zeros present in 98!. Can you give a theorem which says how the number of zeros in x and in 99 times x are related? Gerhard "Ask Me About System Design" Paseman, 2012.07.20 – Gerhard Paseman Jul 21 at 3:47

EDIT: this doesn't really work. I'm still a good human being.

Evenly enough, it seems possible to get the number of zeros in the binary expansion of $n!$

One can get a fairly accurate expression for $$\log_2 \; n! = \frac{\log \; n!}{\log 2}$$ from using extra terms in Stirling's formula. Taking the floor of that and adding 1 gives the total number of digits in base two..

Legendre's formula $$v_2(n!) = \left\lfloor \frac{n}{2} \right\rfloor + \left\lfloor \frac{n}{4} \right\rfloor + \cdots$$ has a companion,

$$v_p(n!) = \frac{n - S_p(n)}{p-1}$$ where $S_p(n)$ is the sum of the digits when $n$ is written in base $p.$ As all the digits in a base two expansion are $1,$ we find that $S_2(n)$ is simply the count of 1's in the base two expansion of $n.$

Alright, some people, who shall remain nameless, have attempted to cast aspersions on the reputation of your humble servant, pointing out that the number of ones in the binary expansion of $n!$ is not the same as the number of ones in the binary expansion of $n$ itself. I try so hard. Don't change the light bulb, I'll just sit here in the dark.

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That would be nice if it were the count of $1$'s in the base two expansion of $n!$. – Robert Israel Jul 13 at 3:51
Well, crap. ${}{}{}{}{}$ – Will Jagy Jul 13 at 3:57
Maybe we can do something with $v_p(n!!)$ – SJR Jul 13 at 7:21

Given a prime $p$, it occurs $m$ times in the prime factorization of $n!$, where

m = $\lfloor \frac{n}{p} \rfloor + \lfloor \frac{n}{p^2} \rfloor + \lfloor \frac{n}{p^3} \rfloor + \cdots$

This is explained in many number theory books. Apply this for $p=2$ and $p=5$, and use the value you get for 5, since this occurs many fewer times.

Tom

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 Well, this is just the simple answer for the trailing zeroes. I know no way to get ALL the zeroes. – Tom Dickens Jul 13 at 2:57 Thanks but that was not what i was asking for. Your solution only applies to the trailing zeroes while i wanted to know all of the zeroes. – Omnitic Jul 13 at 2:58