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# Thread: [SOLVED] 3, 5, 7 primes

1. Originally Posted by dwsmith
I don't like the confusion of n and then having n+2 and n+4. That is why I set S is equiv and then choose the appropriate element of S.
You have a set congruent to an integer modulo another integer. This makes no sense. For example, let A = {1,2,3,4,5,8}.

Solve for x: $A \equiv x\ (\text{mod}\ 3)$.

This is meaningless.

2. Originally Posted by dwsmith
If $n+2\equiv 1 \ (\text{mod} \ 3)$, then $n\neq 1$ since $1+2=3\not\equiv 1 \ (\text{mod} \ 3)$
My apologies. I do not mean that N+2 is congruent to 1(mod3); I mean that if you suppose that N is congruent to 1(mod3) (and thus is of the form 3k+1), then N+2 will be congruent to 0(mod3), which would make your second odd integer not prime. The same reasoning follows if N is congruent to 2(mod3), N+4 will fail to be prime.

These are the three cases Undefined is speaking of.

That is why I said S is equiv and then choose the appropriate element of S.
You do not have to do all that though. What Undefined (I believe) is trying to convey, is that your starting odd integer has to belong to one of three classes: 0, 1 or 2(mod3). It can not belong to 0, as that would make it non-prime. If it belongs to 1(mod3), then one of your other integers will fail (the second one). If it belongs to 2(mod3) then the other integer will fail (the third one). Your then done, as you've shown that all cases result in a list that includes at least one non-prime.

3. Originally Posted by undefined
You have a set congruent to an integer modulo another integer. This makes no sense. For example, let A = {1,2,3,4,5,8}.

Solve for x: $A \equiv x\ (\text{mod}\ 3)$.

This is meaningless.
But why you said $n\equiv \dots$ and then picked {n,n+2, or n+4} to take the place of n that to me makes no sense because n=n+2 for the substitution to work.

4. Originally Posted by dwsmith
But why you said $n\equiv \dots$ and then picked {n,n+2, or n+4} to take the place of n that to me makes no sense because n=n+2 for the substitution to work.
I did not substitute. I was stating an implication ( $\Longrightarrow$).

IF n is congruent to 1 (mod 3), THEN n + 2 is congruent to 0 (mod 3).

5. Originally Posted by undefined
I did not substitute. I was stating an implication ( $\Longrightarrow$).

IF n is congruent to 1 (mod 3), THEN n + 2 is congruent to 0 (mod 3).
Look at post 7 and 8 when I asked about the substitution.

6. Originally Posted by dwsmith
Look at post 7 and 8 when I asked about the substitution.
Oh, I was reading "sub in" loosely as in,

first we had n to the left of the congruence sign

then we had n + 2 to the left of the congruence sign

so n + 2 was "subbed into" the place holder that is on the left of the congruence sign.

I certainly did not mean to say that $n \equiv n+2\ (\text{mod}\ 3)$. (Which can never be true.)

7. Originally Posted by undefined
Oh, I was reading "sub in" loosely as in,

first we had n to the left of the congruence sign

then we had n + 2 to the left of the congruence sign

so n + 2 was "subbed into" the place holder that is on the left of the congruence sign.

I certainly did not mean to say that $n \equiv n+2\ (\text{mod}\ 3)$. (Which can never be true.)
That is why I decided to change n equiv to set with elements to avoid such issues.

Saying x is equiv such that x is some integer and then picking n, n+2, n+4 may be a better method.

8. The final question is how does this justify that there is/are no other groupings of 3 consecutive odd integers?

9. By this bit here, with n as an arbitrary starting integer:

Originally Posted by undefined
It is easiest to make the three cases:

Case 1: $n \equiv 0\ (\text{mod}\ 3)$

Case 2: $n \equiv 1\ (\text{mod}\ 3)$

Case 3: $n \equiv 2\ (\text{mod}\ 3)$
All cases lead to a contradiction of the assumption that there is a set of consecutive odd prime triples that is not "3, 5, 7".

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# Screw Gauge Measurement

Introduction for Screw Gauge Measurement:

Screw gauge: The screw gauge is used to measure the lengths of the given object accurately. Thickness of wire, plate and sheet of paper can be accurately determined using the screw gauge. The lengths are measured by finding the distance advanced by the tip of a fine screw.

 Related Calculators gauge pressure to absolute pressure calculator How to Measure Frequency Measurement Calculator Repeated Measures Anova Calculator

## Construction of Screw Gauge Measurement:

The screw gauge is in the shape of a U which is in metal frame.A hollow cylinder with fixed thread cut inside is attached to one end of the metal frame. A fine screw can work inside the cylinder. The screw gauge also has a pitch scale. A pitch scale is a millimeter scale, marked on the cylinder which is parallel to the axis of the screw.

A sleeve with a beveled edge is attached to the head of the screw and the edge is divided into 100 equal divisions which is called as head scale. The tip of the screw has a plane surface. A stud with a plane parallel surface is fixed to the other end of the U-shaped frame. A ratchet attached to the head of the screw prevents excessive tightening of the screw.

## Principle of the Screw Gauge Measurement:

The principle of screw is used for working the screw gauge. When a screw working inside a fixed nut is rotated over an axis its tip advances through a distance proportional to the number of rotations of the screw.

The linear distance through which the tip moves for one rotation is equal to the distance among any two consecutive threads which is called pitch of the screw.

Pitch and least count of a screw gauge:

Put the zero of the head scale coincide with any division of the pitch scale and now write down the reading of pitch scale. Now produce 10 full rotations to the head scale and now write the change in the pitch scale reading.

Therefore the pitch is written as

Pitch = Distance moved on the pitch scale / Number of rotations

Distance moved by the screw gauge for 10 rotations = 10 mm

Distance moved by the screw gauge for one rotation = (10)/(10) =1 mm

Then the pitch = 1 mm

Least count: When  the screw is turned through 1 division of the head scale the distance moved by the tip of the screw is called least count of the screw.

That is, the least count= Pitch of the screw / Number of head scale decisions.

= 1/(100) =0.01 mm

## Measurement of Thickness of a Wire Using the Screw Gauge:

The measurement of head scale reading is = corrected head scale coincidence xx Least count

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# Acute CODE

Geometry Level 4

In triangle $$ABC$$, $$\angle BAC = 36 ^ \circ$$ and $$\angle ABC = 66 ^\circ$$. Let $$\Gamma$$, with center $$O$$, be the incircle of triangle $$ABC$$. Let points $$D$$ and $$E$$ be the points of tangency between $$\Gamma$$ and lines $$AB$$ and $$AC$$, respectively. What is the acute angle between lines $$CO$$ and $$DE$$ (possibly extended)?

×


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# Convergence in probability of iid normal random variables

Let $X_1, X_2,\ldots$ be a sequence of iid normal random variables with zero mean and unit variance. I read the following as a trivial example: (1) $X_n \to X_1$ in law, (2) $X_n \not\to X_1$ in probability.

So for the first one, I suppose since $F_{X_n}(x) = F_{X_1}(x)$, for every $n$, there is nothing to show as $n\to \infty$ . Is that right?

I do not know how to show the second (does not converge in probability). I know the definitions and some ideas but not sure if they are true. If somebody gives an idea of how to prove second, that would be wonderful. Thanks!

• Are the random variables supposed to be independent? Because, in general, $X_n \not \to X_1$ in probability does not hold. (Simply consider $X_n := X_1$ for some random variable $X_1 \sim N(0,1)$.) – saz Jun 7 '14 at 5:52
• Exactly, thanks, they should be iid. – user48547 Jun 7 '14 at 8:42

In order to prove that convergence in probability does not hold, notice that $X_n-X_1$ is Gaussian and its variance is $2$. Therefore $\mathbb P\{|X_n-X_1|>2\delta\}=\mathbb P\{|N|>\delta\}>0$ where $N$ is normally distributed with mean zero and unit variance. Therefore, there is not convergence in probability to $X_1$ (or any other random variable).
• Hi Davide. I was just trying to check that $\mathbb P\{|X_n-X_1|>2\delta\}=\mathbb P\{|N|>\delta\}$. It turns out, for the right part of the equality, I find an $\epsilon > 0$ which concludes the same proof as above but $\epsilon \neq \delta$ in my case. In other words, I find $P\{|N|>\epsilon\}$ but $\epsilon \neq \delta$. There is another multiplicative factor. Am I wrong? Just checking. thanks! – user48547 Jun 9 '14 at 17:36
• I don' think it's problematic. How is this $\varepsilon$ related to $\delta$? – Davide Giraudo Jun 9 '14 at 17:44
• $\epsilon = \frac{\sqrt{2}}{2}\delta$ in my calculation. – user48547 Jun 9 '14 at 17:50


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# How do you simplify i^100?

Apr 25, 2018

${i}^{100} = 1$

#### Explanation:

${i}^{100} = {\left({i}^{2}\right)}^{50}$

From the fact that ${i}^{2} = - 1 ,$ we get

${\left(- 1\right)}^{50} = 1$ as $- 1$ raised to any even power is $1.$

Alternatively, we can rewrite in trigonometric form and then in the form $r {e}^{i \theta}$:

$i = \cos \left(\frac{\pi}{2}\right) + i \sin \left(\frac{\pi}{2}\right)$

$= {e}^{i \frac{\pi}{2}}$

Raise the exponential to the power of $100 :$

${\left({e}^{i \frac{\pi}{2}}\right)}^{100} = {e}^{50 \pi}$

$= \cos \left(50 \pi\right) + i \sin \left(50 \pi\right)$

$= \cos 2 \pi + i \sin 2 \pi$

$\cos 2 \pi = 1 , \sin 2 \pi = 0$

so we get

$= 1$

Apr 25, 2018

${i}^{100} = 1$

#### Explanation:

${i}^{100} = {\left({i}^{2}\right)}^{50} = {\left(- 1\right)}^{50} = 1$

${\left(- a\right)}^{n} = {a}^{n}$, where n is an even number.


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On Birch and Swinnerton-Dyer's conjecture for elliptic curves with complex multiplication. I
Compositio Mathematica, Volume 37 (1978) no. 2, p. 209-232
@article{CM_1978__37_2_209_0,
author = {Arthaud, Nicole},
title = {On Birch and Swinnerton-Dyer's conjecture for elliptic curves with complex multiplication. I},
journal = {Compositio Mathematica},
publisher = {Sijthoff et Noordhoff International Publishers},
volume = {37},
number = {2},
year = {1978},
pages = {209-232},
zbl = {0396.12011},
mrnumber = {504632},
language = {en},
url = {http://www.numdam.org/item/CM_1978__37_2_209_0}
}

Arthaud, Nicole. On Birch and Swinnerton-Dyer's conjecture for elliptic curves with complex multiplication. I. Compositio Mathematica, Volume 37 (1978) no. 2, pp. 209-232. http://www.numdam.org/item/CM_1978__37_2_209_0/

[1] N. Arthaud: On Birch and Swinnerton-Dyer's conjecture for elliptic curves with complex multiplication II (in preparation).

[2] J. Coates: p-Adic L-functions and Iwasawa's theory (to appear in Proceedings of Durham symposium on algebraic number theory). | Zbl 0393.12027

[3] J. Coates, A. Wiles: Kummer's criterion for Hurwitz numbers (to appear in Proceedings of International Conference on algebraic number theory, Kyoto, Japan, 1976). | Zbl 0369.12009

[4] J. Coates, A. Wiles: On the conjecture of Birch and Swinnerton-Dyer (to appear in Inventiones Mathematicae). | MR 463176 | Zbl 0359.14009

[5] S. Lang: Algebraic Number Theory, Addison-Wesley, 1970. | MR 282947 | Zbl 0211.38404

[6] G. Robert: Unités elliptiques. Bull. Soc. Math. France, Mémoire 36, 1973. | Numdam | MR 469889 | Zbl 0314.12006

[7] G. Shimura: Introduction to the arithmetic theory of automorphic functions. Pub. Math. Soc. Japan, 11, 1971. | MR 314766 | Zbl 0221.10029


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# Thread: Matrix characteristic equation help

1. ## Matrix characteristic equation help

let M=[3,1,0;1,2,1;0,1,3] where ; specifies a new row

show that the characteristic equation is f(x)=(3-x)(x-4)(x-1)

Find det(M-xI) which is:
det[(3-x),1,0;1,(2-x),1;0,1,(3-x)]
=(3-x)((2-x)(3-x)-1)-1((3-x)(0)
=(3-x)(3-x)(2-x)-(3-x)
This expands to -x^3+8x^2-20x+15..which is not the same as the expanded form of the given equation..which is -x^3+8x^2-19x+12....

where have i gone wrong...

Also would the eigenvalues for the characteristic equation be 3, 4 and 1?

2. Hello,

Originally Posted by deragon999
let M=[3,1,0;1,2,1;0,1,3] where ; specifies a new row

show that the characteristic equation is f(x)=(3-x)(x-4)(x-1)

Find det(M-xI) which is:
det[(3-x),1,0;1,(2-x),1;0,1,(3-x)]
=(3-x)((2-x)(3-x)-1)-1((3-x)(0)
Here is the mistake :

It's ok for $\displaystyle (3-x)((2-x)(3-x)-1)$
But the second term is $\displaystyle -1((3-x){\color{red}-}0)$

--> \displaystyle \begin{aligned} f(x) &=(3-x)((2-x)(3-x)-1)-1(3-x) \\ &=(3-x)(6-5x+x^2-2) \\ &=(3-x)(4-5x+x^2) \\ &=(3-x)(4-x)(1-x) \end{aligned}

Also would the eigenvalues for the characteristic equation be 3, 4 and 1?
Yes

3. ## Tks

Omg that makes me look like a dumbass after getting it right in the first half...
neways thanks for ur help on both my latest questions..and many others besides.


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Pilgrim

## Installscript: Get IIS WebSites with WMI

I am trying to a list of websites from the local machine that IIS has available. I am trying to use the CoGetObject to access WMI but i cannot get it to work any ways that i have been able to find online. Ultimately i am trying to get the Virtual Directory path for any current website that may exist on the users machine before install or upgrade.

What i have tried so far is not working for me. Anyone have something working with IIS 7.5 on Win7 x64?

`set oIISRoot = CoGetObject("IIS://localhost/W3SVC","");`

`set oIISRoot = CoGetObject("winmgmts:\\.\root\CIMV2", "");`

`set oIISRoot = CoGetObject("IIS://localhost/W3SVC/1/ROOT");I have had limited success on some machines with this`

I've tried these same pieces of code for GetObject as well with no success
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Pilgrim

## Re: Installscript: Get IIS WebSites with WMI

Anyone have any suggestions?
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Intrepid explorer

## Re: Installscript: Get IIS WebSites with WMI

From a command prompt or bat file do this:
`set "appcmd=%windir%\system32\inetsrv\appcmd.exe"%appcmd% list site`
Pilgrim

## Re: Installscript: Get IIS WebSites with WMI

rguggisberg wrote:
From a command prompt or bat file do this:
`set "appcmd=%windir%\system32\inetsrv\appcmd.exe"%appcmd% list site`

I ended up taking this route. appcmd.exe can handle what i need it too. Thanks


text:
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Look back at the example DFT decomposition in Fig. Successive application of this algorithm obviously yields an N-point Fourier analysis in 10g2 N doublings, and therefore, takes N log2 N operations. The space derivatives are calculated in the wavenumber domain by multiplication of the spectrum with. Begin with time-limited signal x(t), we want to compute its Fourier Transform X(o). 4 Worked Example: Heat Flow in a Nonuniform Rod without Sources 5. This section of MATLAB source code covers Decimation in Frequency FFT or DFT matlab code. IEEE Trans. Demonstrates the proper way to average and measure noise. Cooley and John W. For math, science, nutrition, history. Transforming these eight real points to the frequency domain results in five complex values. com 5 PG106 November 18, 2015 Chapter 1 Overview The Discrete Fourier Transform IP core implements forward and inverse DFTs for a wide range of user-selectable point sizes. For example, let's say the largest size FFT software routine you have available is a 1024-point FFT. The discrete Fourier transform (DFT) is the most direct way to apply the Fourier transform. Online FFT calculator, calculate the Fast Fourier Transform (FFT) of your data, graph the frequency domain spectrum, inverse Fourier transform with the IFFT, and much more. FFT is algorithm used to solve DFT with smaller time. The size of the window dictates the resolution of the resulting spectrum, that is the number of frequency bins in the spectrum will increase linearly with the number of samples we transform. Finite frequency resolution: The DFT of a sequence of length N xprovides a decomposition into Fourier components that are separated by f= 1=(N x). Fourier series Part 2: Square wave example Posted on August 15, 2013 by Gordan Šegon As promised in the first part of the Fourier series we will now demonstrate a simple example of constructing a periodic signal using the, none other then, Fourier series. For a real challenge, try to understand the FFT. The convergence criteria of the Fourier transform (namely, that the function be absolutely integrable on the real line) are quite severe due to the lack of the exponential decay term as seen in the Laplace transform, and it means that functions like polynomials, exponentials, and trigonometric functions all do not have Fourier transforms in the. The discrete Fourier transform, or DFT, is the primary tool of digital signal processing. FFT-Based Algorithm for Metering Applications, Application Note, Rev. The DFT coe cients are denoted X(k). ; Kopayev, V. As an example, such a design could be used for real-time tracking of a narrow-band rogue transmission that is rapidly frequency-hopping across a wide-band range. 10) should read (time was missing in book):. You can check your answers in the table at the end of the 8-point DFT section. For example, with the TZQ basis, the mean unsigned errors for the TMAE4, MLBE4, AE6, and DBE14 bond energy databases are 29. The recursive FFT is given by the following simple Matlab code which must be saved as "fftre-. Y = fft(X) returns the discrete Fourier transform (DFT) of vector X, computed with a fast Fourier transform (FFT) algorithm. 5 or 1, and. It is just a scaling factor. Introduction to FFT & DFT Discrete Fourier Transform (DFT) Digital Image Processing 1 - 7 basic functions Digital Image Processing 2 - RGB image & indexed image Digital Image Processing 3 - Grayscale image I Digital Image Processing 4 - Grayscale image II (image data type and bit-plane) Digital Image Processing 5 - Histogram equalization. Whereas a 2048 sequence will require 11 stages, storing 2048 values each. Let samples be denoted. With today’s modern computers, the differences in speed are not as noticeable in the past. Digital signal processing is a branch of the science of the signal processing. The number of frequencies corresponds to the number of pixels in the spatial domain image, i. Pseudospectral Methods - Summary. Take the discrete Fourier transform of the complex-valued vector. FTN-DFT-S-OFDM systems. It turns out that, under certain conditions, the DFT is just equally-spaced samples of the DTFT. Example 8-5: Consider the 10-point DFT of q[n] = [n 14] which should be Q [k] = e j0:2 (14 )k by virtue of the DFT pair given in ( ?? ). Even though the original 2048 points contain more information, the greater number of samples in the spectrum dilutes the information by the same factor. 5 Hz with frequency range 0 to 511. The core supports input data widths of 8 to 18 bits. The DIT Butterfly is the core. The design can configure the transform length at runtime (on a block-by-block basis) to any one of the 53 sizes specified by. From the mathematical point of view. Ans: The problems u faces while inserting test points , I don't think there is any problem, except 1. increase the number of points acquired at the same sampling frequency. kn = 5 cycles back around to kn = 1, so. how does tool treat this Z as in DFT. Provide details and share your research! But avoid … Asking for help, clarification, or responding to other answers. 5 F, Hz 0 1k 2k 5k 10k 0 50 100 150 200 250 300 350 400 450 500 0 10 20 30 40 50 60 70 80. I assume 1D DFT/IDFT All DFT's use this formula: X(k) is transformed sample value (complex domain) x(n) is input data sample value (real or complex domain) N is number of samples/values in your dataset ; This whole thing is usually multiplied by normalization constant c. 5 FFT implementation The procedure of computing the discrete series of an N-point DFT into two N/2-point DFTs may be adopted for computin g the series of N/2-point DFTs from items of N/4-point DFTs. 4 Quantization Effects in Computing the DFT skip 6. Part 1: The very basics: what is DFT, and what problems does it solve? Tickets, Fri, Apr 3, 2020 at 5:00 PM | Eventbrite. Cooley-Tukey proposed radix-r algorithms, which reduce the N-point DFT computational complexity to O(N log r N). Using a longer DFT does nothing to help this problem. , cosine real parts and sine imaginary. b)(5 points) Choose values for the block size p, the sampling frequency f s and the input to your system to generate at the output music with frequency components. The model is as a MATLAB function dft_3p3r_model() and is defined in the file dft_3p3rmodel. Notes on Fourier Transforms For example, the Hann window for an N point sample w(n)=0. It is a linear invertible transfor-mation between the time-domain representation of a function, which we shall denote by h(t), and the frequency domain representation which we shall denote by H(f). The Fourier series terms diminish in amplitude as 1/n 2, so 5 harmonics should get us within 4% or so of the actual curve. 0633e-07 seconds. Lustig, EECS UC Berkeley Info • Last time - Finished DTFT Ch. Four points of the Fourier analysis lie within the main lobe of corresponding to each sinusoid. If a Fourier map is calculated using data to 60° 2θ, then the low-resolution map shown below is obtained. His major contribution, presented in The Analytical Theory of Heat (1822), was to the theory of heat diffusion in solid bodies. 5]) % Define axes to better visualize signals. A characteristic of the discrete Fourier transform is that the frequency domain is taken from 0 to (N-1)∆f. but we require licence for DFT Compiler. For example, kn = 4 cycles back to kn=0, so the value is 1. In the limit, the rigorous mathematical machinery treats such linear operators as so-called integral transforms. The Discrete Fourier Transform (DFT) is the primary analysis tool for exploring this perspective. This is common in Fourier maps, especially from powder diffraction data, owing to the approximations made in obtaining both F(obs) and φ(obs). Provide details and share your research! But avoid … Asking for help, clarification, or responding to other answers. For example, we may have to analyze the spectrum of the output of an LC oscillator to see how much noise is present in the produced sine wave. 2 Verifying : Examples 5. Active 5 years, 2 months ago. The only points in the interval −L ≤ x ≤ L. The point is that the high order 8 £8 matrix multiplication can be replaced by several 4 £4 matrix multiplications. Although this seems to be a round. The space derivatives are calculated in the wavenumber domain by multiplication of the spectrum with. If so, it calculates the discrete Fourier transform using a Cooley-Tukey decimation-in-time radix-2 algorithm. For my example I'll work with a sequence that equals 1 for and equals 0 elsewhere. If the number of data points is not a power-of-two, it uses Bluestein's chirp z-transform algorithm. CHEM6085 Density Functional Theory 7 Lattice with a basis Example: alpha quartz (SiO 2) The simulation cell with its primitive lattice vectors and its basis The crystal is made from an infinite number of simulation cells •The lattice vectors define the Bravais lattice •The atoms in each cell define the "basis" of. Apart from initialisation most of the code is written in ARM assembler for speed. Some FFT software implementations require this. An FFT is a "Fast Fourier Transform". 3 16 - 24 256 32 =8. The student will be able to: Describe what a layered network communication model is, and describe at least one such model in detail. (DFT) Figure 5. Next the centroid contour distance curve (CCDC) and Fourier descriptors are. The Dirac delta, distributions, and generalized transforms. uk/yzhang Yu Zhang 0002 Pennsylvania State University, University Park, PA, USA Harvard. I assume 1D DFT/IDFT All DFT's use this formula: X(k) is transformed sample value (complex domain) x(n) is input data sample value (real or complex domain) N is number of samples/values in your dataset ; This whole thing is usually multiplied by normalization constant c. Stan-dard versions of the DFT and/or the FFT are available in audio processing software. Integral of sin (mt) and cos (mt) Integral of sine times cosine. Adding n=4 and 5 shows fairly good reconstruction. If we take the 2-point DFT and 4-point DFT and generalize them to 8-point, 16-point, , 2r-point, we get the FFT algorithm. We know the effect of sampling in time domain: L8. The next stage produces N/8 8-point DFTs, and so on, until a single N-point DFT is produced. We require K ≥ N. 1 Dimensionality When the two-dimensional pattern is only structured in one dimension, that also. 32, 5 (1983), 444--450. See also the TransXChange Samples which provide further examples of using TransXChange from live systems. Using a phone or a sat nav when driving. Lustig, EECS UC Berkeley Info • Last time - Finished DTFT Ch. The following are floating-point numbers: The last example is a computer shorthand for scientific notation. The generic example to keep in mind in what follows is. x= [3; 2; 5; 1] 1. 1) The derivation is based on taking the Fourier transform of of (5. Even though the data is real, complex-valued DFT algorithms can still be used. , OFDMA) or other high peak to average power ratio (PAPR) waveform and one or more SC (SC) waveform (e. 4,096 16,769,025 24,576 1,024 1,046,529 5,120 256 65,025 1,024 N (N-1)2 (N/2)log 2 N. Apply for or renew a Blue Badge. The future of designing PCBs to proactively consider DFT could look like this (Figure 5): DFT and testability starts at schematic capture. x [n] is not restricted to be zero mean; it may have a non -zero, complex mean. x = ones(1, 5). means the discrete Fourier transform (DFT) of one segment of the time series, while modi ed refers to the application of a time-domain window function and averaging is used to reduce the variance of the spectral estimates. a ﬁnite sequence of data). Just as a glass prism may display the spectrum of an incoming light wave, Fourier transforms break a signal down into its frequency components. You'll notice that I'm using examples with N as a power of 2. Let us take two signals x 1n and x 2n, whose DFT s are X 1ω and X 2ω respectively. 1024 samples is a common window size. Fast compilation: Compilation seemed quick, albeit Frequon Invaders was a small project. Question: In Class Another Example Of Kernel Transform, Known As The Fourier Transform Was Mention In This Problem We Explore The Fourier Transform And Solve An ODE With It. For the even function, the Fourier series is called the Fourier Cosine series and is given by. Embodiments of a dynamic downlink waveform switching implementation may, for example, support utilization of one or more multiple carrier (MC) waveform (e. Area over head If enable pin of tri-state is 0, the output is Z. The space derivatives are calculated in the wavenumber domain by multiplication of the spectrum with. the right end point removed). The DFT presented here was a forward transform (going from the time domain to the frequency domain). 973 Communication System Design 2 Cite as: Vladimir Stojanovic, course materials for 6. Digital signal processing is a branch of the science of the signal processing. The DIT Butterfly is the core. Another example comes from image processing. Active 5 years, 2 months ago. From the butterfly diagram we see that c(5) is calculated using the following formula; We saw above that: and: and: So substituting these numbers into the equation:. 71:-135 which is just another way to represent the output of the fft() R function. Both G[k] and H[k] can be computed by (N/2)-point DFT, where G[k] is the (N/2)-point DFT of the even numbered points of the original sequence and the second being the (N/2)-point DFT of the odd-numbered point of the original sequence. and the DFT matrix can be found to be: We see that the first component is proportional to the sum of the two signal samples representing the average or DC component of the signal, and second is proportional to the difference between the two samples. For 512 evenly sampled times t (dt = 0. transport secretary Grant Shapps has announced an ambitious £2 billion plan to boost cycling and walking both during and after the lockdown. Ghosh, PK and Jain, PK (1993) An Algebra of Geometric Shapes, IEEE Computer Graphics and Applications, vol 13 pp 50-59, issue 5. It presents a mathematical proof of what is the magnitude of an N-point discrete Fourier transform (DFT) when the DFT's input is a real-valued sinusoidal sequence. The Fourier Analysis tool calculates the discrete Fourier transform (DFT) or it's inverse for a vector (column). where x is the input sequence, X is the DFT, and n is the number of samples in both the discrete-time and the discrete-frequency domains. The following program demonstrates the use of the Radix 2 FFT functions. the periodic extension will also be continuous and hence at these points the Fourier series will in fact converge to the function. 5 or 1, and. Define a complex-valued vector using the coordinates obtained. Invariant properties of the shuffle-exchange and a simplified cost-effective version of the Omega network. Schlembach. Introduction. As shown in Fig. Calculate the FFT (Fast Fourier Transform) of an input sequence. -Evaluation by taking the Discrete Fourier Transform (DFT) of a coefficient vector -Interpolation by taking the "inverse DFT" of point-value pairs, yielding a coefficient vector -Fast Fourier Transform (FFT) can perform DFT and inverse DFT in time Θ(𝑛log𝑛) •Algorithm 1. What problems u faced while inserting test points. 4 you will see that the DFT is essentially the first equation of the finite Fourier series pair. Fast Fourier Transform Algorithms. 11), that is, (10. Fourier Transforms of Discrete Signals Microlink IT College ambawb 2. by Geoff Patterson. The Fourier transform of a sequence, commonly referred to as the discrete time Fourier transform or DTFT is not suitable for real-time implementation. EF-SAGA risk score variables for predicting inadequate safety margin derived from 1,642 consecutive patients undergoing ICD implantation and DFT testing. Running the Fixed-Point Model for the DFT/IDFT Reference Design The fixed-point MATLAB model allows fast bit-accurate simulation of the design’s arithmetic behavior. 86 °C kg/mol Solution: To find the temperature change elevation of a solvent by a solute, use the freezing point depression equation: ΔT = iK f m. Approximate risk of inadequate safety margin ranged from 0% with a score of 0 points to 8. For this case, transform the FFT x-axis point spacing to δf = 1/Δt = 1/0. The constant term is chosen in this form to make later computations simpler, though some other authors choose to write the constant term as a0. Fourier descriptors inherit several properties from the Fourier transform. The pairwise similarity of DFT points is no coincidence. 1 Convergence of Fourier Series † What conditions do we need to impose on f to ensure that the Fourier Series converges to f. Such predictions would be useful for computer-assisted reaction mechanism generation and organic synthesis planning. Using a fast million-point transform allows such local-ization in a single step at a fast refresh rate. Find N-point inverse DFT of fX[k]gN 1 k=0 where X[k] = 8 <: e|˚; k = k0 e |˚; k = N k0. FFT(X) is the discrete Fourier transform (DFT) of vector X. You just use the distributive law and work it out. The PosiTest DFT is a simple, economical solution for those who have no need for the innovative features of the PosiTector 6000 Standard or Advanced models including higher resolution and accuracy, internal memory, PosiSoft software compatibility and universal probe interchangeability. DFT Examples For understanding what follows, we need to refer to the Discrete Fourier Transform (DFT) and the effect of time shift in frequency domain first. Even though the data is real, complex-valued DFT algorithms can still be used. That is 24 in all. architectures for the 3780-point DFT in DMB-T have been proposed [5,6]. On an interval of length 2ℓ, the frequencies (8. With the following trick you can combine the results of multiple 1024-point FFTs to compute DFTs whose sizes are greater than 1024. And it is also fun to use Spiral Artist and see how circles. Recall that we can get the result of multiplying two polynomials by the process of evaluating both at a sufficient number of points, doing pair-wise multiplication on the evaluation values, and then using interpolation to construct the solution polynomial. – Using the NumPy linspace() routine puts a point at both the start and end of the interval e. a square wave = sin (x) + sin (3x)/3 + sin (5x)/5 + (infinitely) That is the idea of a Fourier series. 5]) % Define axes to better visualize signals. Real-world applications of the Fourier transform pricing formula are discussed in part III. The inverse discrete Fourier transform function ifft also accepts an input sequence and, optionally, the number of desired points for the transform. The cycles shown here for the trajectory 1,2,3,4 is 2. -point DFT-point DFT program example_fftw! Example to call 1-D real FFT routine of FFTW implicit none. For example, consider the three functions whose graph are shown below:. means the discrete Fourier transform (DFT) of one segment of the time series, while modi ed refers to the application of a time-domain window function and averaging is used to reduce the variance of the spectral estimates. It calculates eigenvalues and eigenvectors in ond obtaint the diagonal form in all that symmetric matrix form. the FFT is the algorithm to reduce computation of Discrete Fourier Transform (DFT). energy) prevent two electrons from being at the same point in space and how? (work with a specific example, as the one from the previous question) Date : CHEM6085 Density Functional Theory Please note that in all of the questions below and for the rest of the course, whenever we mention “electronic molecular. 973 Communication System Design 2 Cite as: Vladimir Stojanovic, course materials for 6. Note that in reality comparing speeds of various FFT routines is problematic, many of the reported timings have more to do with specific coding methods and their relationship to the hardware and operating system. Let us take two signals x 1n and x 2n, whose DFT s are X 1ω and X 2ω respectively. Basic Definitions Read more Definition of. For matrices, the FFT operation is applied to each column. and what Discrete Fourier Transform will do for us is that it will transform the dataset of {x} into another dataset {X} which will contain the Fourier coefficients such that : If we look at the definition of Fourier Transform, each X in {X} is a complex number and it contains the a and b components for the frequencies. Each Example uses the image generated, using the same technique as above. 5 F, Hz 0 1k 2k 5k 10k 0 50 100 150 200 250 300 350 400 450 500 0 10 20 30 40 50 60 70 80. 30, 5 (1981. What problems u faced while inserting test points. 1/8th of a Hz, as expected, since there are 8 raw data points 1 second apart). It is possible to compute N-point discrete Fourier transforms (DFTs) using radix-2 fast Fourier transforms (FFTs) whose sizes are less than N. Given: density of water at 35 °C = 0. Examples Two-point. Partitioning takes place up to the point where the nodes contain only examples of one class or examples of distinct classes that cannot be distinguished by their attributes. Discrete Fourier Series & Discrete Fourier Transform Chapter Intended Learning Outcomes (i) Understanding the relationships between the transform, sample points of are considered. So :180 means that that cycle starts at the initial rotation of 180 degrees, or $$\pi$$ radians. The DFT of the four points. Alternatively, if the sampling rate had been 10. The fast Fourier transform (FFT) is a very efficient algorithm for calculating the discrete Fourier transform (DFT) of a sequence of data. The PosiTest DFT is a simple, economical solution for those who have no need for the innovative features of the PosiTector 6000 Standard or Advanced models including higher resolution and accuracy, internal memory, PosiSoft software compatibility and universal probe interchangeability. Fessler,May27,2004,13:14(studentversion) FT DTFT Sum shifted scaled replicates Sum of shifted replicates DTFS Z DFT Sinc interpolation Rectangular window. the first fundamental frequency. What is the frequency f o. For example, consider a square wave. Fast Fourier Transform (FFT) In this section we present several methods for computing the DFT efficiently. Fourier analysis is a method for expressing a function as a sum of periodic components, and for recovering the signal from those components. (And for technical reasons, Fourier transforms naturally live in the world of complex functions, where the value of the function at any point is a complex number. This is the currently selected item. The symmetry properties of DFT can be. Complex Fixed-Point Fast Fourier Transform Optimization for AltiVec™ , Rev. 101-102 1998 41 Commun. This contest task is 64 point FFT, which is used in 802. and the DFT matrix can be found to be: We see that the first component is proportional to the sum of the two signal samples representing the average or DC component of the signal, and second is proportional to the difference between the two samples. The DFT is the sampled Fourier Transform and therefore does not contain all frequencies forming an image, but only a set of samples which is large enough to fully describe the spatial domain image. The Fourier Method can be considered as the limit of the finite-difference method as the length of the operator tends to the number of points along a particular dimension. Based on the optimized T1 geometry, simply use for example "# PBE1PBE/6-31G* TD(triplet)", then from the output file you will find transition energy between S0-T1, which corresponds to. The DFT formula is:. For example, the 127-point FFT could also be computed using computationally efficient 256-point DIT transforms. We shall show that this is the case. The PSF is also called the impulse response of the system. Power Spectrum Density based on Fourier Spectrum¶ default_NFFT = 4096¶ default number of samples used to compute FFT. For example, let's say that the rightmost dimension is longitude and has size of mlon=72. 2) required to represent a function in Fourier series form are equally distributed, with interfrequency spacing ∆k = kν+1 − kν = π ℓ. Engineering Tables/Fourier Transform Table 2 From Wikibooks, the open-content textbooks collection < Engineering Tables Jump to: navigation, search Signal Fourier transform unitary, angular frequency Fourier transform unitary, ordinary frequency Remarks 10 The rectangular pulse and the normalized sinc function 11 Dual of rule 10. For example, let's say the largest size FFT software routine you have available is a 1024-point FFT. The standard procedure (procedure 1), applicable at PBE level, is also described in Fcc Si bandstructure example. X 7 : * * 5 8 3 3 0. The NTT is a generalization of the classic DFT to finite fields. Spectral Analysis – Fourier Decomposition (Butler Example 2. In this module we continue the discussion on how to speed up the multiplication of larg polyonmials. THEOREM 5 For any two functionsf;g with period1 we have 1. and Shaffer, R. In these example magnitudes, a 128 point DFT cannot resolve the two peaks, while a 512 point DFT can. The Discrete Fourier Transform (DFT) is the primary analysis tool for exploring this perspective. Lecture 7 -The Discrete Fourier Transform 7. Increasing the number of terms in the partial sum does not decrease the magnitude of the overshoot but moves the overshoot extremum point closer and closer to the jump discontinuity. Compute Fˆ(m) = 1 N P N−1 k=0 e −2πimk N F(k) with the minimum amount of ﬂops (=quickly). The object uses one or more of the following fast Fourier transform (FFT) algorithms depending on the complexity of the input and whether the output is in linear or bit-reversed order:. 1) The derivation is based on taking the Fourier transform of of (5. It it does not exist say why: a) x n 0. plot(n, x, 'rs') % The red squares mark the digitized samples. He proposed that any function could be written as an infinite sum of the trigonometric functions cosine and sine; for example, Expressions of this. 3 Linear Filtering Approach to Computing the DFT skip 6. the FFT is the algorithm to reduce computation of Discrete Fourier Transform (DFT). Today, efﬁcient million-point Fast Fourier Transforms (FFTs) are not. 1 Overview The FFT core computes an N-point forward DFT or inverse DFT (IDFT) where N can be 2m, m = 3-16. This page covers 16 point Decimation in Frequency FFT/DFT with Bit reversed OUTPUT. Here's the 8-point DFT of our 8-point rectangular pulse: x = ones(1, M); X = fft(x). The project is actually not so new, I've put it on GitHub more than three months ago, but it had some issues I had to solve and also I did not have patience until now to write a new blog entry. From the mathematical point of view. FTN-DFT-S-OFDM systems. transport secretary Grant Shapps has announced an ambitious £2 billion plan to boost cycling and walking both during and after the lockdown. Chapter 3: Problem Solutions Fourier Analysis of Discrete Time Signals Problems on the DTFT: Definitions and Basic Properties àProblem 3. This book serves two purposes: 1) to provide worked examples of using DFT to model materials properties, and 2) to provide references to more advanced treatments of these topics in the literature. For a real challenge, try to understand the FFT. If you glance back to Section 4. Example 8-5: Consider the 10-point DFT of q[n] = [n 14] which should be Q [k] = e j0:2 (14 )k by virtue of the DFT pair given in ( ?? ). We shall show that this is the case. Stan-dard versions of the DFT and/or the FFT are available in audio processing software. X 5 , X 6 and. N2/mul-tiplies and adds. Schlembach. Description: Bandstructure for Si within DFT+HF. On the other hand, CART is a decision tree method which is capable of binary partitioning only. Note that in reality comparing speeds of various FFT routines is problematic, many of the reported timings have more to do with specific coding methods and their relationship to the hardware and operating system. , The Integral Converges. 10) should read (time was missing in book):. the subject of frequency domain analysis and Fourier transforms. 8 1 The Fourier Transform: Examples, Properties, Common Pairs Odd and Even Functions Even Odd f( t) = f(t) f( t) = f(t. DFT+U theory¶ The basic idea behind DFT+U is to treat the strong on-site Coulomb interaction of localized electrons, which is not correctly described by LDA or GGA, with an additional Hubbard-like term. Digital Signal Processing - 8 Point DFT (shortcut) Problem - Duration: 9:39. 2 - z-Transforms Ch. 30 points · 5 days ago · edited 5 days ago I know others will disagree, but I think feral druids (esp those that have impt tanking roles) make the most sense getting it first given that warriors/rogues/hunters have a lot of other ways to get hit gear and/or weapon skill to reduce their needed hit. The DFT is usually considered as. If you're behind a web filter, please make sure that the domains *. x1(n) → X1(ω) and x2(n) → X2(ω) Then ax1(n) + bx2(n) → aX1(ω) + bX2(ω) where a and b are constants. Selecting the best candidate location for the test points. Therefore the Fourier Transform too needs to be of a discrete type resulting in a Discrete Fourier Transform ( DFT ). The DFT: Discrete Fourier Transform The DFT is a linear transformation of the vector xn (the time domain signal samples) to the vector Xm (the set of coefﬁcients of component sinusoids of time domain sig nal) using Xm = NX−1 n=0 xnw nm, (1) where N is the size of the vectors, w= e2iπ/N are the "roots-of-unity" (twiddle factors. So :180 means that that cycle starts at the initial rotation of 180 degrees, or $$\pi$$ radians. Simple Application Examples ECE 5655/4655 Real-Time DSP 10-7 † The DFT points, , are simply a sampled version of (10. It states that the DFT of a combination of signals is equal to the sum of DFT of individual signals. On the other hand, CART is a decision tree method which is capable of binary partitioning only. The source code for this example is in Appendix B. Adding n=4 and 5 shows fairly good reconstruction. For example, consider a square wave. 5]) % Define axes to better visualize signals. Finding Fourier coefficients for a square wave If you're seeing this message, it means we're having trouble loading external resources on our website. 1 Frequency viathe DFT/FFT The spectrum gives importantinformationabout the makeup of a sound and is most commonly implemented in a computer by running a program called the Discrete Fourier Transform (DFT) or the more efﬁcient Fast Fourier Transform (FFT). Consider various data lengths N = 10,15,30,100 with zero padding to 512 points. DS260 March 1, 2011 www. Such numerical computation of the Fourier transform is known as Discrete Fourier Transform (DFT). edge detection, image filtering, image reconstruction, and image compression. I described the relationship between the DFT and the DTFT in my March 15 post. Using a fast million-point transform allows such local-ization in a single step at a fast refresh rate. Introduction to Fourier Series We’ve seen one example so far of series of functions. laz file from the DFT Zenodo repository and uncompress it with LASzip; Start Matlab/Octave; Delete any previous versions of the toolbox. Notes on Fourier Transforms For example, the Hann window for an N point sample w(n)=0. Figure 2-2 Results of an eight-point real-to-complex DFT The five complex values are packed in the output vector shown in Figure 2-3. The FFT algorithm reduces an n-point Fourier transform to about (n/2) log 2 (n) complex multiplications. IEEE Trans. We combine the last two chapters to get to the discrete-time Fourier transform (DTFT) in Chapter 5. Therefore, if I bit reverse the index of sample index 8 (which in binary is 00100) in a 32-point FFT, the new index will remain 8 as reversing the bits of the number 8 in 5-bit. To be specific, if we perform an N -point DFT on N real-valued time-domain samples of a discrete cosine wave, having exactly integer k cycles over N time samples, the peak magnitude. Embodiments of a dynamic downlink waveform switching implementation may, for example, support utilization of one or more multiple carrier (MC) waveform (e. (And for technical reasons, Fourier transforms naturally live in the world of complex functions, where the value of the function at any point is a complex number. EXERCISE 5: Inverse Fourier Transform (IFFT) In this exercise, we are going to use the Matlab Function IFFT. 5 n c) x n 2n u n. Let N be the total number of elements in Array, and decompose N into its prime factors:. 2018 5 5 568--595 Anders S. Fast Fourier Transform. Integral of product of sines. 86 °C kg/mol Solution: To find the temperature change elevation of a solvent by a solute, use the freezing point depression equation: ΔT = iK f m. 1 Frequency viathe DFT/FFT The spectrum gives importantinformationabout the makeup of a sound and is most commonly implemented in a computer by running a program called the Discrete Fourier Transform (DFT) or the more efﬁcient Fast Fourier Transform (FFT). A numerical example may be helpful. 17 s - the phase at = differs. kn = 5 cycles back around to kn = 1, so. See example 6 for noncollinear magnetism, example 7 (and references quoted therein) for spin-orbit interactions. The DFT takes a discrete signal in the time domain and transforms that signal into its discrete frequency domain representation. An FFT is a DFT, but is much faster for calculations. Introduction to FFT & DFT Discrete Fourier Transform (DFT) Digital Image Processing 1 - 7 basic functions Digital Image Processing 2 - RGB image & indexed image Digital Image Processing 3 - Grayscale image I Digital Image Processing 4 - Grayscale image II (image data type and bit-plane) Digital Image Processing 5 - Histogram equalization. I have a new project on GitHub 1. 9% with a score of 4–5 points. Fast Fourier Transform (FFT) In this section we present several methods for computing the DFT efficiently. One example: Fourier transform of transmission electron microscopy images helps to check the periodicity of the samples. com 2 Product Specification LogiCORE IP Fast Fourier Transform v7. Discrete Fourier Series DTFT may not be practical for analyzing because is a function of the continuous frequency variable and we cannot use a digital computer to calculate a continuum of functional values DFS is a frequency analysis tool for periodic infinite-duration discrete-time signals which is practical because it is discrete. 3 16 - 24 256 32 =8. It calculates eigenvalues and eigenvectors in ond obtaint the diagonal form in all that symmetric matrix form. DS260 March 1, 2011 www. 0) mean = the DC value (center pixel) of the magnitude image. To complete one period of the minimum frequency = 5. Description. Problems calculating 8-point FFT of an 8-point sine wave by hand. 1Compute the DFT of the 2-point signal by hand (without a calculator or computer). For large enough L, all the important detail of the Fourier Transform is displayed by the DFT. The 10th anniversary year design theme is Fast Fourier Transform Circuit, which is very famous signal processing technology. Many of the toolbox functions (including Z -domain frequency response, spectrum and cepstrum analysis, and some filter design and. Introduction to the Discrete-Time Fourier Transform and the DFT C. The blog was highly motivated by the youtube post Discrete Fourier Transform - Simple Step by Step and popularity of Spectrogram analysis in Data Science. Fast Fourier Transform Example¶ Figure 10. Y = fft(X) returns the discrete Fourier transform (DFT) of vector X, computed with a fast Fourier transform (FFT) algorithm. Now tides are of course important because they can lead to some trouble and here in Venice is a case in point. The 'Fourier Transform ' is then the process of working out what 'waves' comprise an image, just as was done in the above example. 7] instead of [1 -1], because our cycle isn't exactly lined up with our measuring intervals, which are still at the halfway point (this could be desired!). 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I assume 1D DFT/IDFT All DFT's use this formula: X(k) is transformed sample value (complex domain) x(n) is input data sample value (real or complex domain) N is number of samples/values in your dataset ; This whole thing is usually multiplied by normalization constant c. EE123 Digital Signal Processing Lecture 5 based on slides by J. (a) Calculate by hand the 4-point DFT Xk for k = 0, 1, 2, 3 when x[0] = 1, x[1] = 1, x[2J = 1, x[3] = 1. The DFT of the four points. We know the effect of sampling in time domain: L8. 024 kHz would have yielded ∆f = 0. 11a/g/n Wireless LAN devices. A simple analogy. Stan-dard versions of the DFT and/or the FFT are available in audio processing software. Demonstration of DFT leakage - a tone at 5. IEEE Trans. 5 or 1, and. 0 5 10 15 20-1-0. The DFT is defined as such: X [ k ] = ∑ n = 0 N − 1 x [ n ] e − j 2 π k n N {\displaystyle. Math 201 Lecture 30: Fourier Cosine and Sine Series Mar. liquid includes both algorithms and chooses the most appropriate one for the task. b, e Conventional diffraction-limited point scan imaging of the sample with 390 nm (b) and 490 nm (e) features. For example, if a 2048 point DFT is used, the frequency spectrum becomes 1025 samples long. 5 n c) x n 2n u n. Low pause garbage collector: Go 1. Example 7. Computational Efficiency. 5,10,3); here a is an array of size 8 element to be checked for 0 Hz to 30 Hz with 0. These are combined to form N/4 4-point DFTs. e DFT) to perform fast linear convolution " Overlap-Add, Overlap-Save. Translation invariance: no matter where the shape is located in the image, the Fourier descriptors remain the same. DS260 March 1, 2011 www. 10) should read (time was missing in book):. If you like to buy me a coffee: paypal. This is due to various factors. Notice that this is a constant signal. A characteristic of the discrete Fourier transform is that the frequency domain is taken from 0 to (N-1)∆f. 4 you will see that the DFT is essentially the first equation of the finite Fourier series pair. Examples of Fourier series 12 Example 1. The Fast Fourier Transform (FFT) Algorithm The FFT is a fast algorithm for computing the DFT. Serra 2 Index. The point is that the high order 8 £8 matrix multiplication can be replaced by several 4 £4 matrix multiplications. The Linear System Solver is a Linear Systems calculator of linear equations and a matrix calcularor for square matrices. Example: A basic input file Illustrated in this first example is a very basic file for doing a bulk hexagonal GaN calculation. 2D Discrete Fourier Transform • Fourier transform of a 2D signal defined over a discrete finite 2D grid of size MxN or equivalently • Fourier transform of a 2D set of samples forming a bidimensional sequence • As in the 1D case, 2D-DFT, though a self-consistent transform, can be considered as a mean of calculating the transform of a 2D. me/techfold360 In this video, 4 point discrete fourier transform (DFT) is solved using matrix method. For example, consider a square wave. Arduino: Frequency Transform (DFT): this program is to calculate frequency transform on arduino with batter control over parameters. kn = 5 cycles back around to kn = 1, so. – Using the NumPy linspace() routine puts a point at both the start and end of the interval e. The PSF is illustrated in the lower left corner of the image. edge detection, image filtering, image reconstruction, and image compression. The recursive FFT is given by the following simple Matlab code which must be saved as "fftre-. Approximate risk of inadequate safety margin ranged from 0% with a score of 0 points to 8. If we kept calculating coefficients for higher k, we would find that the power spectrum is reflected around N/2. And the result of an N-point DFT will require twice the memory of the original sequence, assuming that it is stored as floating point real numbers, considerably 16 times the storage is needed if the original sequence is the result of sampling by, say, an 8 bit ADC. Take the discrete Fourier transform of the complex-valued vector. This calculator is online sandbox for playing with Discrete Fourier Transform (DFT). FFT Discrete Fourier transform. The fast Fourier transform (FFT) is a very efficient algorithm for calculating the discrete Fourier transform (DFT) of a sequence of data. The DFT is usually considered as. Then we have five Fourier. Embodiments of a dynamic downlink waveform switching implementation may, for example, support utilization of one or more multiple carrier (MC) waveform (e. 2 – Architecture of a DFT (1 2 0 1 [ ] [ ] N jn k N k x k X n e N Inve rse Discre t e Fourie r Transform DFT) Figure 5. If we kept calculating coefficients for higher k, we would find that the power spectrum is reflected around N/2. Finite frequency resolution: The DFT of a sequence of length N xprovides a decomposition into Fourier components that are separated by f= 1=(N x). I then decided to take a look at Kolmogorov's original article Une série de Fourier–Lebesgue divergente presque partout, and the proof given there uses no difficult theorems; it is of comparable difficulty to de Bois-Reymond's example of a continuous function whose Fourier series diverges at a point, but for some reason the latter proof is. Try the example below; the original sequence x and the reconstructed sequence are identical (within rounding error). Examples $11$ and $12$ can be found in Gradsteyn and Ryzhik. The discrete Fourier transform, or DFT, is the primary tool of digital signal processing. Some examples are if f(x) = e 2x-> enter e^(2*x) if f(x,y) = sin e 2x-> enter sin(e^(2*x)) 4) If the function is defined piecewise, enter the upper limit of the first interval in the field labeled "Sub-interval 1" and enter the function from that point to the next interval if more or "Limit inf. Hypocycloids and pedal curves. The inverse discrete Fourier transform function ifft also accepts an input sequence and, optionally, the number of desired points for the transform. by Geoff Patterson.
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text:
# Maximum resolution per lens size

This question is more practical than theoretical, but I am interested in the theoretical considerations as well.

My wife just bought a Samsung S3 phone with a 8 MP image sensor hiding behind a tiny lens. In daylight the pictures come out fine, but it suffers horribly in low-light conditions. Is there a theoretical limit as to how fine an image sensor can be behind a lens of a specific aperture, given a reasonable amount of ambient light and a reasonable shutter speed? Will increasing the sensor resolution beyond this limit decrease the actual resolution (the ability to resolve two points as individual points) of the final image?

Thanks.

-

$$\Delta \ell = 1.22 \frac{f\lambda}{D}$$
where $f$ is the distance from the plane of the lens to the detector, $\lambda$ is the wavelength of the light and $D$ is the camera aperture. Making the pixel size smaller than $\Delta \ell$ won't do any harm, but it won't make the pictures any sharper.


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# Questions regarding BJT saturation for a circuit

I have the following circuit which converts weak sine signal to pulses:

I have tried it on breadboard and it seems it works fine. In my application freq. is between 1Hz to 30Hz or max 100Hz. And the input signal Vpp will be from 200mV to 2Vpp.

Below is the collector and base currents:

And here below graph zoomed to show Vce which is 50mV during saturation:

Here are my questions:

1) I'm not sure if R2 and R3 is set correct/optimum for using this circuit for switching action even though in practice it works(I set R2 and R3 empirically). Am I oversaturating this transistor? In my second plot above Ic/Ib<10 but in its data sheet at saturation Ic/Ib should be around 10. It is a bit confusing.

Briefly I want to learn how can we calculate R2 and R3 for good saturation and what should be their rough value?

2) All the texts I have seen says Vce is around 0.2 during BJT's saturation but in my simulation(3rd plot) it is only 50mV. Why is that so?

• Before answering I and surely the others, too, want to know what is the intended usage of the generated pulses. No optimization is possible without knowing it. Your generated pulses for example have quite slow ramps for many applications that need pulses which change their state in nanoseconds. – user287001 Aug 31 '17 at 23:34
• Freq will be between 1Hz to 30Hz. And fast rising edges are not important since this will pull down an NPN input of another device which will take care of it. Precision is not important. – user1245 Aug 31 '17 at 23:41
• It is saturating better than Vce(sat)@ ? mA because you are using less current than ? mA. Imagine an internal collector R, we call Rce and then you can estimate Vce(sat) – Tony Stewart Sunnyskyguy EE75 Sep 1 '17 at 0:07
• @user134429 Is this just turning a sine wave into a square wave with perhaps hysteresis? And you really are using a $14.2\:\textrm{V}$ power supply? And this is driving yet another NPN circuit? I wouldn't recommend a single CE stage for this, but you say it drives another NPN circuit anyway, so it seems as though you should disclose the 2nd stage so that one might attempt to merge their functions. But up to you. Other than that, it's not clear to me what isn't clear to you. Asking "am I oversaturating" just leaves me wondering without really clarifying your quandary, for example. (To me.) – jonk Sep 1 '17 at 1:05
• @jonk It will drive the NPN input of this: brodersencontrols.com/images/pxf-20_11.pdf 14.2V is the supply from this device(I guess this device will sharpen pulses as well). I could use another supply for the transistor as well. Regarding my circuit, the input range will be 200mVpp to 2Vpp. I checked in real this circuit works but I'm not sure R2 and R3 is set correct/optimum values. If Ic/Ib<10 does that mean something is wrong? Or is there a limit for Ib? How would you set R3 and R2 for the input range I mentioned? – user1245 Sep 1 '17 at 1:15

It is difficult to make a single transistor work as a limiter unless there are limits on input signal range and frequency, so you need to define these limits.

But assuming they are only for the values given, we can make it better.

When your input signal goes low Vbe turns off and the collect current shuts off and Vc is pulled up according the Rc value and ratios.

When your input goes high , collector goes low but it stays low more than half the time so the input is pulled up too much from negative feedback current.

## Solution?

1) Change bias of R2 from 0V to Vcc but with a value of 10x Rc or roughly 20k

• Why? Vce(sat) is normally rated at Ic/Ib=10

2) Change R3 from 20x Rc to 50x Rc or ~ 100K Change Rf

When Vce saturates , its voltage Vce(sat) depends on the collector current as if there was a small series R, which we can call "Rce". This value controls the Vce(sat) and Rce is reduces as device power rating increases. Then it is affected by temperature and chip design so the default spec is Vce(sat) at some rated current. Rce is similar to RdsOn in MOSFETs but not as low. You may estimate this as the rise of Vce(sat) for rise in current as long as base current is at least 5~10% of collector.

## p.s.

Normally 2 devices working in differential mode give a better result then we move up to comparator designs or use a CMOS logic buffered inverter AC Coupled with high R feedback for self biasing for amazing simplicity. with large R values and much small C coupling values. like 10M and 0.1uF

• I made a minor mistake I updated my circuit now. R3 would be directly connected to Vcc. Are you saying R2 better 20k and R3 100k? In my application freq. is between 1Hz to 30Hz or max 100Hz. And the input signal Vpp will be from 200mV to 2Vpp. – user1245 Sep 1 '17 at 0:29
• Input is not fixed. Range is 200mV to 2Vpp. Following your logic, I set R3 to 220k and R2 to 39k; to make things better for the 200mVpp to 2Vpp input range. Do you think makes sense? – user1245 Sep 1 '17 at 1:04
• 2V is driving too much current into Vbe , what is source impedance? WIth that range you need a better limiter than 1 or 2 transistors, BTW the F2V converter is overkill. – Tony Stewart Sunnyskyguy EE75 Sep 1 '17 at 1:35
• I noticed my max input can be 12Vpp – user1245 Sep 1 '17 at 1:50
• this is the sensor I want to use nrgsystems.com/assets/resources/an40C-IF3-interface.pdf together with F2V converter's NPN input – user1245 Sep 1 '17 at 1:53


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# Why is best subset selection not favored in comparison to lasso?

I’m reading about best subset selection in the Elements of statistical learning book.
If I have 3 predictors $x_1,x_2,x_3$, I create $2^3=8$ subsets:

1. Subset with no predictors
2. subset with predictor $x_1$
3. subset with predictor $x_2$
4. subset with predictor $x_3$
5. subset with predictors $x_1,x_2$
6. subset with predictors $x_1,x_3$
7. subset with predictors $x_2,x_3$
8. subset with predictors $x_1,x_2,x_3$

Then I test all these models on the test data to choose the best one.

Now my question is why is best subset selection not favored in
comparison to e.g. lasso?

If I compare the thresholding functions of best subset and lasso, I see that the best subset sets some of the coefficients to zero, like lasso.
But, the other coefficient (non-zero ones) will still have the ols values, they will be unbiasd. Whereas, in lasso some of the coefficients will be zero and the others (non-zero ones) will have some bias.
The figure below shows it better:

From the picture the part of the red line in the best subset case is laying onto the gray one. The other part is laying in the x-axis where some of the coefficients are zero. The gray line defines the unbiased solutions. In lasso, some bias is introduced by $\lambda$. From this figure I see that best subset is better than lasso! What are the disadvantages of using best subset?

In subset selection, the nonzero parameters will only be unbiased if you have chosen a superset of the correct model, i.e., if you have removed only predictors whose true coefficient values are zero. If your selection procedure led you to exclude a predictor with a true nonzero coefficient, all coefficient estimates will be biased. This defeats your argument if you will agree that selection is typically not perfect.

Thus, to make “sure” of an unbiased model estimate, you should err on the side of including more, or even all potentially relevant predictors. That is, you should not select at all.

Why is this a bad idea? Because of the bias-variance tradeoff. Yes, your large model will be unbiased, but it will have a large variance, and the variance will dominate the prediction (or other) error.

Therefore, it is better to accept that parameter estimates will be biased but have lower variance (regularization), rather than hope that our subset selection has only removed true zero parameters so we have an unbiased model with larger variance.

Since you write that you assess both approaches using cross-validation, this mitigates some of the concerns above. One remaining issue for Best Subset remains: it constrains some parameters to be exactly zero and lets the others float freely. So there is a discontinuity in the estimate, which isn’t there if we tweak the lasso $\lambda$ beyond a point $\lambda_0$ where a predictor $p$ is included or excluded. Suppose that cross-validation outputs an “optimal” $\lambda$ that is close to $\lambda_0$, so we are essentially unsure whether p should be included or not. In this case, I would argue that it makes more sense to constrain the parameter estimate $\hat{\beta}_p$ via the lasso to a small (absolute) value, rather than either completely exclude it, $\hat{\beta}_p=0$, or let it float freely, $\hat{\beta}_p=\hat{\beta}_p^{\text{OLS}}$, as Best Subset does.

This may be helpful: Why does shrinkage work?


text:
Is boric acid a protic acid? Explain.

Asked by Pragya Singh | 1 year ago |  49

##### Solution :-

No, it's an acid, but it's not one of the protic ones. As a Lewis acid, it's a weak monobasic acid with a low pH.

Because it accepts two electrons from the $$OH^{-}$$ ion, it behaves like an acid.

Answered by Abhisek | 1 year ago

### Related Questions

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Give reason: Aluminium utensils should not be kept in water overnight.

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Give reason: Aluminium alloys are used to make aircraft bodies.


text:
# (howto) Perform local realignment around indelsTutorials | Created 2016-03-08 | Last updated 2017-10-02

This tutorial replaces Tutorial#2800 and applies to data types within the scope of the GATK Best Practices variant discovery workflow.

We provide example data and example commands for performing local realignment around small insertions and deletions (indels) against a reference. The resulting BAM reduces false positive SNPs and represents indels parsimoniously. First we use RealignerTargetCreator to identify and create a target intervals list (step 1). Then we perform local realignment for the target intervals using IndelRealigner (step 2).

## 1. Introduction and tutorial materials

#### Why do indel realignment?

Local realignment around indels allows us to correct mapping errors made by genome aligners and make read alignments more consistent in regions that contain indels.

Genome aligners can only consider each read independently, and the scoring strategies they use to align reads relative to the reference limit their ability to align reads well in the presence of indels. Depending on the variant event and its relative location within a read, the aligner may favor alignments with mismatches or soft-clips instead of opening a gap in either the read or the reference sequence. In addition, the aligner's scoring scheme may use arbitrary tie-breaking, leading to different, non-parsimonious representations of the event in different reads.

In contrast, local realignment considers all reads spanning a given position. This makes it possible to achieve a high-scoring consensus that supports the presence of an indel event. It also produces a more parsimonious representation of the data in the region .

This two-step indel realignment process first identifies such regions where alignments may potentially be improved, then realigns the reads in these regions using a consensus model that takes all reads in the alignment context together.

#### Prerequisites

• Installed GATK tools
• Coordinate-sorted and indexed BAM alignment data
• Reference sequence, index and dictionary
• An optional VCF file representing population variants, subset for indels

• To download the reference, open ftp://ftp.broadinstitute.org/bundle/b37/ in your browser. Leave the password field blank. Download the following three files (~860 MB) to the same folder: human_g1k_v37_decoy.fasta.gz, .fasta.fai.gz, and .dict.gz. This same reference is available to load in IGV.
• Click tutorial_7156.tar.gz to download the tutorial data. The data is human paired 2x150 whole genome sequence reads originally aligning at ~30x depth of coverage. The sample is a PCR-free preparation of the NA12878 individual run on the HiSeq X platform. I took the reads aligning to a one Mbp genomic interval (10:96,000,000-97,000,000) and sanitized and realigned the reads (BWA-MEM -M) to the entire genome according to the workflow presented in Tutorial#6483 and marked duplicates using MarkDuplicates according to Tutorial#6747. We expect the alignment to reveal a good proportion of indels given its long reads (~150 bp per read), high complexity (PCR-free whole genome data) and deep coverage depth (30x).

Tutorial download also contains a known indels VCF from Phase 3 of the 1000 Genomes Project subset for indel-only records in the interval 10:96,000,000-97,000,000. These represent consensus common and low-frequency indels in the studied populations from multiple approaches. The individual represented by our snippet, NA12878, is part of the 1000 Genomes Project data. Because of the differences in technology and methods used by the Project versus our sample library, our library has potential to reveal additional variants.

## 2. Create target intervals list using RealignerTargetCreator

For simplicity, we use a single known indels VCF, included in the tutorial data. For recommended resources, see Article#1247.

In the command, RealignerTargetCreator takes a coordinate-sorted and indexed BAM and a VCF of known indels and creates a target intervals file.

java -jar GenomeAnalysisTK.jar \
-T RealignerTargetCreator \
-R human_g1k_v37_decoy.fasta \
-L 10:96000000-97000000 \
-known INDEL_chr10_1Mb_b37_1000G_phase3_v4_20130502.vcf \
-I 7156_snippet.bam \
-o 7156_realignertargetcreator.intervals

In the resulting file, 7156_realignertargetcreator.intervals, intervals represent sites of extant and potential indels. If sites are proximal, the tool represents them as a larger interval spanning the sites.

• We specify the BAM alignment file with -I.
• We specify the known indels VCF file with -known. The known indels VCF contains indel records only.
• Three input choices are technically feasible in creating a target intervals list: you may provide RealignerTargetCreator (i) one or more VCFs of known indels each passed in via -known, (ii) one or more alignment BAMs each passed in via -I or (iii) both. We recommend the last mode, and we use it in the example command. We use these same input files again in the realignment step.

The tool adds indel sites present in the known indels file and indel sites in the alignment CIGAR strings to the targets. Additionally, the tool considers the presence of mismatches and soft-clips, and adds regions that pass a concentration threshold to the target intervals.

If you create an intervals list using only the VCF, RealignerTargetCreator will add sites of indel only records even if SNPs are present in the file. If you create an intervals list using both alignment and known indels, the known indels VCF should contain only indels. See Related resources.

• We include -L 10:96000000-97000000 in the command to limit processing time. Otherwise, the tool traverses the entire reference genome and intervals outside these coordinates may be added given our example 7156_snippet.bam contains a small number of alignments outside this region.
• The tool samples to a target coverage of 1,000 for regions with greater coverage.

#### The target intervals file

The first ten rows of 7156_realignertargetcreator.intervals are as follows. The file is a text-based one-column list with one interval per row in 1-based coordinates. Header and column label are absent. For an interval derived from a known indel, the start position refers to the corresponding known variant. For example, for the first interval, we can zgrep -w 96000399 INDEL_chr10_1Mb_b37_1000G_phase3_v4_20130502.vcf for details on the 22bp deletion annotated at position 96000399.

10:96000399-96000421
10:96002035-96002036
10:96002573-96002577
10:96003556-96003558
10:96004176-96004177
10:96005264-96005304
10:96006455-96006461
10:96006871-96006872
10:96007627-96007628
10:96008204

To view intervals on IGV, convert the list to 0-based BED format using the following AWK command. The command saves a new text-based file with .bed extension where chromosome, start and end are tab-separated, and the start position is one less than that in the intervals list.

awk -F '[:-]' 'BEGIN { OFS = "\t" } { if( $3 == "") { print$1, $2-1,$2 } else { print $1,$2-1, \$3}}' 7156_realignertargetcreator.intervals > 7156_realignertargetcreator.bed

## 3. Realign reads using IndelRealigner

In the following command, IndelRealigner takes a coordinate-sorted and indexed BAM and a target intervals file generated by RealignerTargetCreator. IndelRealigner then performs local realignment on reads coincident with the target intervals using consenses from indels present in the original alignment.

java -Xmx8G -Djava.io.tmpdir=/tmp -jar GenomeAnalysisTK.jar \
-T IndelRealigner \
-R human_g1k_v37_decoy.fasta \
-targetIntervals 7156_realignertargetcreator.intervals \
-known INDEL_chr10_1Mb_b37_1000G_phase3_v4_20130502.vcf \
-I 7156_snippet.bam \
-o 7156_snippet_indelrealigner.bam

The resulting coordinate-sorted and indexed BAM contains the same records as the original BAM but with changes to realigned records and their mates. Our tutorial's two IGV screenshots show realigned reads in two different loci. For simplicity, the screenshots show the subset of reads that realigned. For screenshots of full alignments for the same loci, see here and here.

• The -targetIntervals file from RealignerTargetCreator, with extension .intervals or .list, is required. See section 1 for a description.
• Specify each BAM alignment file with -I. IndelRealigner operates on all reads simultaneously in files you provide it jointly.
• Specify each optional known indels VCF file with -known.
• For joint processing, e.g. for tumor-normal pairs, generate one output file for each input by specifying -nWayOut instead of -o.
• By default, and in this command, IndelRealigner applies the USE_READS consensus model. This is the consensus model we recommend because it balances accuracy and performance. To specify a different model, use the -model argument. The KNOWNS_ONLY consensus model constructs alternative alignments from the reference sequence by incorporating any known indels at the site, the USE_READS model from indels in reads spanning the site and the USE_SW model additionally from Smith-Waterman alignment of reads that do not perfectly match the reference sequence.

The KNOWNS_ONLY model can be sufficient for preparing data for base quality score recalibration. It can maximize performance at the expense of some accuracy. This is the case only given the known indels file represents common variants for your data. If you specify -model KNOWNS_ONLY but forget to provide a VCF, the command runs but the tool does not realign any reads.

• If you encounter out of memory errors, try these options. First, increase max java heap size from -Xmx8G. To find a system's default maximum heap size, type java -XX:+PrintFlagsFinal -version, and look for MaxHeapSize. If this does not help, and you are jointly processing data, then try running indel realignment iteratively on smaller subsets of data before processing them jointly.
• IndelRealigner performs local realignment without downsampling. If the number of reads in an interval exceeds the 20,000 default threshold set by the -maxReads parameter, then the tool skips the region.

#### Changes to alignment records

For our example data,194 alignment records realign for ~89 sites. These records now have the OC tag to mark the original CIGAR string. We can use the OC tag to pull out realigned reads and instructions for this are in section 4. The following screenshot shows an example pair of records before and after indel realignment. We note seven changes with asterisks, blue for before and red for after, for both the realigned read and for its mate.

Changes to the example realigned record:

• MAPQ increases from 60 to 70. The tool increases each realigned record's MAPQ by ten.
• The CIGAR string, now 72M20I55M4S, reflects the realignment containing a 20bp insertion.
• The OC tag retains the original CIGAR string (OC:Z:110M2I22M1D13M4S) and replaces the MD tag that stored the string for mismatching positions.
• The NM tag counts the realigned record's mismatches, and changes from 8 to 24.

Changes to the realigned read's mate record:

• The MC tag updates the mate CIGAR string (to MC:Z:72M20I55M4S).
• The MQ tag updates to the new mapping quality of the mate (to MQ:i:70).
• The UQ tag updates to reflect the new Phred likelihood of the segment, from UQ:i:100 to UQ:i:68.

RealignerTargetCreator documentation has a -maxInterval cutoff to drop intervals from the list if they are too large. This is because increases in number of reads per interval quadratically increase the compute required to realign a region, and larger intervals tend to include more reads. By the same reasoning, increasing read depth, e.g. with additional alignment files, increases required compute.

Our tutorial's INDEL_chr10_1Mb_b37_1000G_phase3_v4_20130502.vcf contains 1168 indel-only records. The following are metrics on intervals created using the three available options.

               #intervals    avg length     basepair coverage
VCF only       1161           3.33           3,864
BAM only        487          15.22           7,412
VCF+BAM        1151          23.07          26,558

You can project the genomic coverage of the intervals as a function of the interval density (number of intervals per basepair) derived from varying the known indel density (number of indel records in the VCF). This in turn allows you to anticipate compute for indel realignment. The density of indel sites increases the interval length following a power law (y=ax^b). The constant (a) and the power (b) are different for intervals created with VCF only and with VCF+BAM. For our example data, these average interval lengths are well within the length of a read and minimally vary the reads per interval and thus the memory needed for indel realignment.

## 4. Related resources

• See the Best Practice Workflow and click on the flowchart's Realign Indels icon for best practice recommendations and links including to a 14-minute video overview.
• See Article#1247 for guidance on using VCF(s) of known variant sites.
• To subset realigned reads only into a valid BAM, as shown in the screenshots, use samtools view 7088_snippet_indelrealigner.bam | grep 'OC' | cut -f1 | sort > 7088_OC.txt to create a list of readnames. Then, follow direction in blogpost SAM flags down a boat on how to create a valid BAM using FilterSamReads.
• See discussion on multithreading for options on speeding up these processes. The document titled How can I use parallelism to make GATK tools run faster? gives two charts: (i) the first table relates the three parallelism options to the major GATK tools and (ii) the second table provides recommended configurations for the tools. Briefly, RealignerTargetCreator runs faster with increasing -nt threads, while IndelRealigner shows diminishing returns for increases in scatter-gather threads provided by Queue. See blog How long does it take to run the GATK Best Practices? for a breakdown of the impact of threading and CPU utilization for Best Practice Workflow tools.
• See DePristo et al's 2011 Nature Genetics technical report for benchmarked effects of indel realignment as well as for the mathematics behind the algorithms.
• See Tutorial#6517 for instructions on creating a snippet of reads corresponding to a genomic interval. For your research aims, you may find testing a small interval of your alignment and your choice VCF, while adjusting parameters, before committing to processing your full dataset, is time well-invested.
• The tutorial's PCR-free 2x150 bp reads give enough depth of coverage (34.67 mean and 99.6% above 15) and library complexity to allow us the confidence to use aligner-generated indels in realignment. Check alignment coverage with DepthofCoverage for WGS or DiagnoseTargets for WES.
• See SelectVariants to subset out indel calls using the -selectType INDEL option. Note this excludes indels that are part of mixed variant sites (see FAQ). Current solutions to including indels from mixed sites involves the use of JEXL expressions, as discussed here. Current solutions to selecting variants based on population allelic frequency (AF), as we may desire to limit our known indels to those that are more common than rare for more efficient processing, are discussed in two forum posts (1,2).
• See Tutorial#6491 for basic instructions on using the Integrative Genomics Viewer (IGV).


text:
Molar Heat Capacities of Ideal Gases

Nathaniel 2E
Posts: 27
Joined: Mon Jun 25, 2018 3:00 am

Molar Heat Capacities of Ideal Gases

In question 8.31 from the 6th addition, the solutions manual explains that for monatomic ideal gases at constant pressure, the molar heat capacity is (5/2)R, and for a monatomic ideal gases at constant volume, the molar heat capacity is (3/2)R. Why can we assume these two claims to be true?

Chem_Mod
Posts: 17455
Joined: Thu Aug 04, 2011 1:53 pm
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Re: Molar Heat Capacities of Ideal Gases

$C{v} = \frac{3}{2}R$
$C{p} = \frac{5}{2}R$
These are the constants for molar heat capacities that we use when we are working with ideal gases. In that problem, it stated to assume that krypton behaves as an ideal gas, and so it is safe to assume that we can use Cv and Cp. R is the gas constant 8.314 J/(K*mol).