# Questions tagged [fourier-analysis]

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

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### 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 ...
913 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 ...
156 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 ...
178 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 ...
997 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 ...
15k 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 ...
2k 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 ...
3k 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, ...
738 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 ...
2k 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 ...
362 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 ...
1k 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: ...
925 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 ...
19k views

### Calculate the 2D Fourier transform of an Image

I am new to Mathematica, and using version 8.0. I would like to calculate the 2D Fourier Transform of an Image with Mathematica and plot the magnitude and phase ...
2k 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 ...
885 views

### Next highly composite number?

R language has this function 'nextn' (link) which computes the next highly composite number greater than a given one, which is used to find the optimal padding size for the subsequent FFT operation. ...
2k 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 ...
6k views

### Computation of Hankel Transform using FFT (Fourier)

To address circularly symmetric cases of 2-D Fourier Transformations, the so-called Hankel Transform can be applied (for a detailed derivation of the relation between the 2-D Fourier transform and the ...
154 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)) ...
1k 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 ...
559 views

### FourierSeries for rational function looks wrong

Bug introduced in Version 8 or earlier, and persisting through 12.1. I have the following code: ser[x_] = FourierSeries[(π^2 + a)/(3 x^2 + a), x, 10] // N // Chop ...
2k 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 ...
256 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 ...
866 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 ...
3k 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, ...
3k 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 ...
4k 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, ...
1k 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: ...
7k views

### Usage of Assuming for Integration

For some reason, when I enter the following integration in Mathematica Assuming[{k ∈ Integers}, Integrate[ Exp[ I k t], {t, -π, π}]] the result turns out to be 0....
18k 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 ...
2k views

### Problem with Fourier coefficients

I have just started using Mathematica with v9.0. I am trying to follow a computation from a book on Fourier series with the function $f(x)=x$ on the interval $-\pi < x < \pi$. Here is the code ...
932 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 <...
3k 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 ...
1k views