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

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9
votes
0answers
304 views

Proving (self) similarity with Mathematica - Reccurrence Plots, Similarity Plots etc

I posted this question in math.se but given the sheer tumultuous number of questions that keep appearing on math.se and also given that I am trying to accomplish this in Mathematica, I thought I'd ...
5
votes
1answer
198 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: $ ...
1
vote
0answers
50 views

Fourier transform an expression to obtain a distribution?

I have this expression for the correlation function for a rigid rotating molecule: $G(\tau) = 4 \pi \int \omega ^2 P_2[\cos (\omega \tau)] P(\omega) \, \mathrm{d}\omega \quad [1]$ where $P_2$ is a ...
0
votes
1answer
146 views

Programming a recursive FFT with Mathematica

I'm trying to program a FFT using a recursive function in Mathematica, though my program is not getting me anywhere at the moment. Could you say what's wrong with it and what I can do to make it work? ...
0
votes
1answer
63 views

How to set up the Fourier domain for a Fourier Transform? [duplicate]

I am having trouble understanding how to set up the grid in the Fourier domain, while performing Discrete Fourier Transforms. This might be a very trivial question, but I'd appreciate any help ...
0
votes
0answers
28 views

Issues with zero frequency component in discrete Fourier transform

I'm having trouble with the Fourier function at the moment. I'm solving a set of differential equations with NDSolve, then need to extract the spectrum associated with the curve below: So i use ...
2
votes
0answers
59 views

Workarounds for a possible bug in the linearity of FourierTransform

This is somewhat similar to this question, except the problem I am encountering is to do with Fourier transforms of scalar multiples of functions and their derivatives. I wish to input ...
3
votes
4answers
391 views

Why does Fourier give a shifted frequency?

I have a signal that I want to identify the frequencies in it, I used the Fourier function but I can't get the frequency correctly. Here is a simplified example: ...
3
votes
2answers
126 views

Fourier Analysis: How to get rid of a discontinuity

When I compute the phase error of a spatial series data using Fourier analysis in Mathematica there's a discontinuity @ parameter ...
5
votes
1answer
104 views

How to plot stability region of Fourier analysis

Stability limits for Runge–Kutta methods in the complex ΩΔt-plane are needed to be plotted like this: For example, let P=1+z where ...
0
votes
0answers
29 views

Discrete Fourier Normalization

I have a problem using the Fourier command applied to the square of an exponential function. I would like to compare the theoretical result (called ...
3
votes
3answers
139 views

Fitting the Plot by fourier Series of either sine or cosine

I have list of data and its plot and I don't know how to fit the plot with fourier series of either sine or cosine. Full Data: ...
-1
votes
1answer
58 views

Ploting fourier transform [closed]

I want to Find the fourier transform of this graph. {ListLinePlot[hari, PlotRange -> {{0, 200000}, {-1.5, 1.8}}]} And when I Put: ListLinePlot[Abs[Fourier[hari][[2 ;; 100]]], PlotRange -> All, ...
0
votes
0answers
25 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
votes
0answers
63 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
votes
2answers
179 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
vote
2answers
95 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
votes
1answer
44 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
votes
0answers
87 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
vote
0answers
69 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
votes
0answers
36 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 ...
10
votes
3answers
285 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
votes
0answers
77 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 ...
2
votes
1answer
79 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 ...
11
votes
2answers
195 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 ...
0
votes
0answers
54 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 ...
13
votes
4answers
1k 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 ...
10
votes
1answer
787 views

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

I'm trying to Fourier transform a one dimensional list of a time history of some quantity using the Fourier function. I'm interested in the frequency spectrum, but ...
2
votes
0answers
57 views
3
votes
1answer
233 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
177 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
vote
2answers
143 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
votes
0answers
111 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
239 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, ...
0
votes
2answers
105 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 ...
1
vote
1answer
226 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
votes
0answers
66 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 ...
4
votes
1answer
229 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
votes
1answer
264 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
votes
1answer
122 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? ...
6
votes
0answers
126 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
vote
1answer
146 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 $[-\pi,\pi]$, ...
10
votes
2answers
848 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
187 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
vote
1answer
70 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
votes
1answer
111 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
157 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
93 views
0
votes
1answer
82 views

Is there a way to plot discrete functions in mathematica? [closed]

Suppose you have a discrete function Triangle[n/5]. How would you plot it in mathetica?