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

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16
votes
4answers
1k views

Digital filter of image in Fourier space

Consider the contour plot below, of a function f(x,y) - which is calculated numerically by solving some equations. If one looks carefully, one can observe two types of waves, to the left and right of ...
9
votes
1answer
2k views

Computation of Hankel Transform using FFT (Fourier)

To address circular symmetric cases of 2D Fourier Transformations the so called Hankel Transform can be applied (for a detailed derivation of the relation between the 2D Fourier transform and the 1D ...
2
votes
1answer
107 views

Tough Inverse Fourier Integral: why does the sign matter?

I'm computing the Inverse Fourier Integral of ((a^2 + omega ^2) c^2) /((b^2 + omega^2) ((r^2 + omega^2 - omegaInt^2)^2 + (2 omegaInt r)^2)) ...
0
votes
1answer
357 views

How to manipulate a Fourier sine series?

I would like to plot the Fourier sine series for $f(x) = x$. I would like to manipulate the parameter n from $0$ to $10$ and plot the sine waves over $(0,1)$. My ...
9
votes
1answer
435 views

FourierSeries for rational function looks wrong

I have the following code: ser[x_] = FourierSeries[(\[Pi]^2 + a)/(3 x^2 + a), x, 10] // N // Chop It gives me some series, which I then try to plot. And ...
2
votes
1answer
900 views

Fourier transform of sampled data

I have got some impulse response data that I would like to transform via Fourier to get the amplitude-frequency characteristics of the performing loudspeaker. The ...
0
votes
1answer
152 views

Error messages when using NInverseFourierTransform

I have two functions that I need to inverse Fourier transform and I was trying to get Mathematica to help me. I tried simply using theInverseFourierTransform ...
1
vote
0answers
503 views

Doing local FFT on huge 3D vector data cell mesh and visualizing it spatially?

Simulation type: I'm running a simulation with the OOMMF micromagnetics package http://math.nist.gov/oommf/ where are magnet is represented by a mesh of 3 million cells, it gets excited by a ...
1
vote
2answers
1k views

Discrete FFT of non-periodic signal excited by short pulse

Say I have a signal F(t) which represents a excitation by a pulse (so it is not periodic and declining to zero amplitude). According to this answer, for instance, ...
0
votes
1answer
704 views

How can I find the Fourier series from discrete data?

I would like to define the function with Fourier series when I just have discrette data. (I don't have a specific function). I can draw the graph using the data, but I don't have a idea how can I get ...
11
votes
3answers
2k views

How to approximate a given WAV file with trigonometric series?

I'd like (together with a few people) to prepare a presentation about Fourier series for middle/high school students. I thought it might be quite cool to play a violin sound from, say, a WAV file, ...
1
vote
1answer
513 views

Fourier transformation of solution of differential equation

I'm trying to plot a Fourier transform of solution of differential equation. I have tried with: ...
10
votes
2answers
8k views

Plotting the frequency spectrum of a data series using Fourier

testData = Table[N@Sin[500 x], {x, 0, 100}]; ListLinePlot[Abs[Fourier[testData]], PlotRange -> Full] Gives me Which I do not expect because the Fourier ...
12
votes
1answer
548 views

How can I obtain a zero-filled Fourier transform, as produced by MATLAB's fft?

The MATLAB FFT function, fft(X,n), can be used to return the n-point DFT. This effectively extends the original signal, X, to ...
3
votes
2answers
1k views

Obtaining the Fourier transform of an operator

We know that if we have a function $f(x)$, and we call $g(\omega)$ its Fourier transform, then the Fourier transform of $x f(x)$ is $$\imath \frac{\mathrm{d} g(\omega))}{\mathrm{d}\omega} $$ and ...
7
votes
1answer
611 views

Speeding up numerical Fourier Transform

I wrote this function NFourierTransform, which takes a function $f(k)$ and numerically calculates the fourier transform integral for discrete values of $k \in ...
2
votes
0answers
303 views

Fourier Coefficients in Mathematica [duplicate]

I'm calculating Fourier Coefficients by hand and trying to verify them in Mathematica. However, in Mathematica I get them wrong by a factor of 2. Is there some part of the Mathematica functions I'm ...
1
vote
2answers
898 views

How to calculate FDCT

I'm new to Mathemtica and I'm trying to calculate Discrete Cosine Transformation FDCT. I found the FourierDCT built-in function, but not DCT, so I need to implement it. I have tried couple of ideas ...
10
votes
0answers
353 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 ...
7
votes
2answers
2k views

Fourier Transform of a Step Function

I'm trying to obtain the form of a sinc function that I know I'm supposed to get in Mathematica. I'm doing this because I intend to do a lot with Fourier transforms (FT) and I'd like to know I'm not ...
1
vote
1answer
1k views

discrete Fourier transform

As an answer to my code I will get a periodic discrete time dependent function called "data" which I want to get a Discrete Fourier transform of it using just one period of it,but I think some thing ...
20
votes
2answers
2k views

How to make Fourier behave like FourierTransform?

I'm not very experienced with Fourier Transforms, so there may be something inherently wrong with attempting to do this, but how can I make the discrete Fourier behave like the continuous ...
1
vote
2answers
2k views

Computing the minimum number of terms required in a Fourier series to achieve a particular upper bound on the error

In a Fourier series, the maximum error bound is the difference of the function and the partial sum of its Fourier series. Within an interval, as we increase the number of terms of partial sums, the ...
7
votes
2answers
200 views

Speed up Fourier for Booleans

I'm calculating a bit of the power spectrum of a two color cellular automaton using: ...
13
votes
1answer
4k views

Coulomb potential as a Fourier transform

It is well known from theory that the Coulomb potential can be obtained as a Fourier transform in the following way: $$ \int \frac{\mathrm{d}^3p}{\left( 2 \pi \right)^3} \frac{e^{\mathrm{i} ...
19
votes
3answers
2k views

Can one find the beat of a tune with Fourier analysis?

I'm trying to find out if it's possible to find the beat of a tune by Fourier analysis with Mathematica. I'm taking a 44.1 kHz sample sound and hoping that I might get a nice peak for a frequency ...
12
votes
2answers
287 views

Parallelization of distinct array write access from subkernels

I'm working on an implementation of a multivariate FFT, which is (or at least should be) highly parallelizable due to the row-column-algorithm. However, i can't figure out how to implement that. The ...
8
votes
3answers
5k views

Plotting Partial Sums of Fourier Series

I'd like to plot some partial sums for a Fourier Series problem, but I am not sure if the output I am getting is correct. I want to be able to plot the partial sums and the function on the same graph. ...
17
votes
4answers
4k views

Numerical Fourier transform of a complicated function

Say I have a function $f(x)$ that is given explicitly in its functional form, and I want to find its Fourier transform[1]. If $f$ is too complicated to have an analytic expression for $\hat f(k)$, how ...
7
votes
2answers
5k views

Does Mathematica implement the fast Fourier transform?

Is there a fast Fourier transform in Mathematica? Although looking in the help I could not find one. I am looking to implement the equivalent of fft in MATLAB.