Questions on the discrete and continuous Fourier analysis functions of Mathematica, as well as the FourierSeries` package.

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26 views

Why I am not getting the same frequency when sampling a waveform? [duplicate]

I am trying to simulate the sampling of a waveform to then apply FFT Analysis to it. Here is the sample code I have now using a square wave: ...
0
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0answers
71 views

Calculating the recursion at the Fourier domain

I would like to calculate the following recursion with mathematica $$f_n(x)=\int_{B}^{A}f_{n-1}(x-\omega)f(\omega)\mbox{d}\omega\quad\quad f_1(w):=f(w)$$ This is simply the convolution of $f$ with ...
3
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2answers
237 views

Integration and Fourier transform

I would like to calculate the distribution function from the characteristic function. There is a formula given as $$F_X(x)=\frac{1}{2}+\frac{1}{2\pi}\int_{0}^\infty \frac{e^{i w x}\phi(-w)-e^{-i w ...
1
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2answers
268 views

Fourier series for rectangular wave incorrect, why?

I'm trying to get the fourier series function(s) to work for a square wave with duty cycles other than 50% ie rectangular wave. ...
0
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1answer
63 views

What should I expect for Fourier transform of Sinc? [closed]

I was expecting something I could interpret as a rect function. I don't think the Dirac delta function qualifies — for one thing, I think that would be the transform of a constant. ...
3
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0answers
147 views

How to do Fast Fourier transform (FFT) for singular functions?

I want to do a 3-dimensional FFT on this function $\frac{\cos (x) \cos (y) \cos (z)-\sin (x) \sin (y) \sin (z)}{\left((1.0001+\sin (y)+\cos (z))^2+(0.0001+\cos (x)+\sin (z))^2+(0.0001+\sin (x)+\cos ...
1
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0answers
98 views

Is it the right output for Fourier?

I am learning Fourier Series at university so I wanted to do something with Mathematica to calculate frequency spectrum and harmonics of whatever function I create. This is what I have until now after ...
3
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0answers
63 views

What are good/best practices to take the Fourier transform of an InterpolatingFunction?

I have a function which I have obtained from numerical integration of a differential equation, and I would like to take its Fourier transform. What are good practices for doing this? To make things ...
6
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1answer
313 views

calling CUDA library functions

Mathematica has some predefined CUDA functions, like CUDAMap, CUDAFourier, etc. My question is how can one call functions which are part of CUDA library but not part of predefined Mathematica ...
0
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1answer
84 views
12
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3answers
368 views

Disentangling the data

An experiment yields a functional dependence on two variables $F(x,y)$, can be imagined as a 2D map. It is known that the function can be factored as follows $F(x,y)=fx(x) gy(y) +gx(x) fy(y)$. Given ...
2
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1answer
182 views

Sampling a musical instrument (or re-tuning MIDI)

I'd like to try to convert a piece of MIDI music made with SoundNote to another tuning (not microtonal or even split-black-keys, just a slightly different tuning for each note). I searched for pitch ...
0
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0answers
91 views

Discrete Fourier Transform and data manipulate

I solve a system od ODE and i save the discrete solution (i.e.: x,y,vx,vy, or a subset of it) in a file. Then i try to call the DFT on this file but the problem is that i must have also the time in ...
11
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2answers
301 views

Rotational Averaging of Image Periodograms (FFTS)

I'm writing a code to do rotational averages of image FFT's. I have a working version but it is pretty slow. Wondering if anyone has any thoughts on a way to do this more efficiently. Data looks ...
14
votes
4answers
3k views

Plotting Fourier spectrum versus frequency of a signal

I have looked around here, and i am sure this has been answered, but i don't understand it. The thing is, I have taken a introductory signal processing course, and we had to use Mathematica, and i had ...
2
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0answers
67 views

Why does setting $Assumptions make my Fourier transforms slow?

Consider these Fourier transforms ...
6
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2answers
439 views

Correct fourier scaling and high-resolution frequency identification

I have a dataset of amplitude versus time $(t,A(t))$ and I need to extract the dominant frequency and amplitude, and also get the amplitude at one other specific frequency. My data looks like this: ...
4
votes
1answer
201 views

Reconciling results from Fourier with those form FourierTransform

I need to use the discrete Fourier transform for function that represented as list of values. I started with an easy task to check my understanding. I tried to get the amplitude values for ...
1
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2answers
231 views

2D Fourier transform of a table - ArrayPlot issue

Recently, I have encountered an issue with ArrayPlot after performing a Fourier transform of a table. Picture presented above is an ArrayPlot of a 2D table. Using Fourier on this 2D table I obtain ...
3
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0answers
143 views

Fourier transformation of HeavisideTheta functions

I want to find 2D-Fourier transformation of the function given below f = HeavisideTheta[y1]*HeavisideTheta[y2 - y1] For the purpose, I use built-in function in ...
5
votes
1answer
442 views

Fit data with linear combinations of Cos and Sin

Recall that if $f$ is a piecewise continuous function on the interval $[-\pi, \pi]$, then the Fourier series of $f$ is $$f(x) = \sum_{n=0}^{\infty} (a_n \cos(nx) + b_n \sin(nx)).$$ See for example, ...
1
vote
1answer
685 views

Plot Fourier transform of $\sin (2 t)$

I'm trying to plot the Fourier transform of $\sin (2 t)$. I tried using the FourierTransform Function (I'm expecting a peak at w = 2) but it gives me undefined at ...
0
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0answers
83 views

Recognizing a generalized function as zero

Consider the following expression: HeavisideTheta[x]HeavisideTheta[-x] Mathematica will not simplify it further. But $\Theta(x)\Theta(-x)$ is zero if considered ...
5
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1answer
288 views

Extracting frequencies with Fouriertransformation

I know this question came up so many times, but after browsing through many of the threads, I'm still not sure, if I'm doing it correctly with my dataset, so I'll give it a try. If have some sample ...
3
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1answer
448 views

How do you use fourier transforms to perform a deconvolution

I've been trying to teach myself about deconvolution through fourier transforms, but I seem to be missing something simple, as my results are garbage. I start by defining a test function and a window ...
0
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2answers
130 views

How to obtain the form of sin(nx) and cos(nx) from the result of FourierSeries [closed]

How to obtain the form of sin(nx) and cos(nx) from the result of FourierSeries[]. For Example, $$\text{FourierSeries}[x,x,5]=i e^{-i x}-i e^{i x}-\frac{1}{2} i e^{-2 i x}+\frac{1}{2} i e^{2 i ...
0
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1answer
193 views

ListLinePlot “Cannot Take Positions” error with Fourier of WAV file

When I try to do a Fourier analysis of a WAV file with a sample rate of 22050 I get an error "Cannot take positions". What am doing wrong? ...
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0answers
156 views

Possible bug with FourierTransform linearity

Each component is easily transformed but the sum is not: FourierTransform[f''[x], x, k] FourierTransform[f'[x], x, k] ...
1
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1answer
393 views

Fourier Series of “Split” Defined Function

Not sure how to phrase this in a concise way, anyway it seems like the function FourierSeries assumes the interval for which to compute the Fourier coefficients of a given function is $[-\pi,\pi]$, ...
5
votes
1answer
244 views

Prove an identity in quantum harmonic oscillator

Problem: In the context of quantum harmonic oscillator the eigenfunctions are given by: $ u_n(x) = (N_n/\sqrt{b}) H_n(x/b) \exp\left[-x^2/(2b^2)\right] $, where $N_n$ is the normalization factor: $ ...
11
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2answers
2k views

Finding fourier transform of data and hence frequencies

I looked at all the other questions related to mine before posting this, and they didn't solve my problem. I have a large data set which can be downloaded from here. I'm using the following code to ...
2
votes
1answer
362 views

Integrate message: can't prove Integration limits are real

I'm working on solving differential equations through Fourier series, I made a function to help me calculate the coefficients that looks like this: ...
1
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1answer
92 views

Two dimensional NIntegration failure - non-numerical values

I've got this function: E0[x0_, y0_, z_]:= A/w[z]*Exp[-(x0^2 + y0^2)/(w[z]*w[z])]*Exp[(I*2*Pi*(x0^2 + y0^2))/(λ*2*R[z])]*Exp[I*ϕ[z]]; Where the ...
0
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1answer
142 views

Fourier-Analysis How to display every period correctly? [duplicate]

I want to express a function as a sum of fourier series. I tried the code below. It works. But only get one period (from 0 to 1). How to display every period correctly? ...
2
votes
1answer
200 views

Why does FourierTransform[] converge while same integral manually written does not?

I'm studying the quantum mechanics of an infinite square well from a computational standpoint. My eigenfunctions are defined as $u_n(x)=\sqrt{2/L}\sin\left(n\pi x/L\right),\quad 0 \le x \le L, \quad ...
3
votes
3answers
96 views

Filling in explicit zeros in a (x,y) list for nonexisting y values for discrete Fourier transform in Mathematica

I have a list of (x,y) values in Mathematica for various discrete x values, as in ...
3
votes
1answer
440 views

Animated Wave Propagation using Fourier & InverseFourier

This is a continuation off of previous help on the first part of my project: fourier issue arising from input miscommunication Now I want to go one step further in the current code. Here's the code ...
0
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2answers
105 views

fourier issue arising from input miscommunication

xdomain = Table[i , {i, -10, 10, .1}]; ListPlot[InverseFourier[ Fourier[E^-#^2 & /@ xdomain]*E^#^2 & /@ xdomain]] So I want to numerically fourier ...
5
votes
0answers
131 views

The same analytical expression gets inconsistent FourierTransform results

I have an expression which is just a linear combination of plane waves, and I'd like to calculate FT of it. I know what I will get should be a bunch of delta functions, but it turns out Mathematica ...
0
votes
1answer
337 views

Plotting partial sums of Fourier sine series

How do I plot this on Mathematica version 5.2? $\frac{4}{\pi} \sin{x} + \frac{4}{3 \pi} \sin{3 x} + \cdots + \frac{4}{(2 N+1) \pi} \sin{(2 N+1) x}$ over $x \in [-\pi,\pi]$ for $N= 3, 6, 12, 24$. I ...
14
votes
1answer
1k views

What's the correct way to shift zero frequency to the center of a Fourier Transform?

I'm trying to apply a Fourier transform of a one dimensional list of a time history of some quantity using the Fourier function. I'm interested in the frequency ...
6
votes
2answers
801 views

Band-pass filter an image

Ok so i have some HR-TEM images. In this technique fringes appear whereever a crystalline structure is present. This fringes are separated by a certain distance depending on the material, this is our ...
4
votes
2answers
760 views

Frequencies represented in a DFT list (Fourier[])

I have a sound sample (sample rate: 44100). When I have a list l with n successive elements from the sample, ...
10
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1answer
455 views

Why does Mathematica return a Fourier transform for a function for which it is not defined?

The following function $$g(x) = (1 + x^{1/a} )^a $$ should NOT have a Fourier transform, as far as I am aware, for any real values of $a$ since $g(x)$ is not nice in the sense of decays quickly ...
5
votes
2answers
762 views

How to draw a graph about the FourierTransform of a 2D Function?

Here is a 2D function, and it cannot be calculated by the FourierTransfrom ...
8
votes
0answers
165 views

Fourier transform over a custom dimension

I have a multidimensional array A. Fourier[A] finds the discrete Fourier transform over all dimensions. How to find discrete ...
8
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2answers
530 views

Why Fourier doesn't show me the peaks?

I'm trying to identify the frequencies in my time history samples, and I can see a frequency in the time history, but can't see it in its Fourier transform. Here it is : the sample data: ...
1
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1answer
414 views

Problem with Fourier and InverseFourier function

I have the following code Image[img, ImageSize -> 300] data = ImageData[img]; fdct = Fourier[data] tdata = InverseFourier[fdct]; Image[tdata] but it seems to ...
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votes
1answer
4k views

Determine the 2D-Fourier transform of an Image

I am new to Mathematica and using Version 8.0. I want to calculate the 2D-Fourier Transform of a digital image and see its Magnitude and Phase Spectrum, and reconstruct it.
9
votes
1answer
728 views

FourierTransform and Partial Derivatives?

I have a function of three variables $f(x,y,z)$, and it obeys a linear partial differential equation. I'm checking my by-hand calculations with Mathematica. I want to convert the PDE into the ...