Mathematica Stack Exchange
Mathematica Stack Exchange

Questions tagged [fourier-analysis]

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

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

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701 questions
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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 FourierTransform? What is the equivelent way of doing the…
EmpireJones
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22
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How to calculate the Fourier Transform of a Gaussian pulse with a nonlinear chirp: Cos[ t + Exp[t^2] ]?

I have an optical pulse in time domain: Exp[-t^2] Cos[50 t - Exp[-2 t^2] 8 π]. The figure of this formula is I hope to calculate the Fourier Transform of this formula, which gives the spectral distribution of this pulse. The spectral shape…
user14634
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18
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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} \mathbf{p} \cdot \mathbf{r}}}{\mathbf{p}^2+m^2} = …
zakk
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16
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2 answers

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.
500
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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 Transform is FourierTransform[Sin[500 x], x, f], I Sqrt[Pi/2] DiracDelta[-500+f]-I Sqrt[Pi/2]…
C. E.
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12
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1 answer

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 Fourier transform over a custom dimension like fft(A,[],dim) function in MATLAB? My current solution: FourierDim[list_,…
ybeltukov
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12
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1 answer

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 Fourier-spectral domain, but Mathematica isn't playing…
rajb245
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10
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1 answer

finding Frequency of Sinewave data using Fourier

CONTEXT I read 5 different related posts but I do not understand how to interpret mathematica's output for my situation. data=(Uncompress@*FromCharacterCode@*Flatten@*(ImageData[#1, "Byte"] &)@* …
Conor
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8
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2 answers

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: dt = 0.01;(*0.01 second per…
xslittlegrass
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8
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1 answer

Fixing phase unwrapping jumps

The problem of unwrapping 1D phase often comes up in Fourier analysis: someone computes a DFT of some data, the resulting phase values fall between $-\pi$ and $\pi$, and they'd like to "unwrap" these phase values to not be bounded to (-$\pi$,$\pi$].…
nadlr
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7
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1 answer

2D Fourier transform

I want to calculate the 2D Fourier transformation of a circular shaped aperture, but Mathematica won't finish the calculation: h[x_, y_] := UnitBox[Sqrt[x^2 + y^2]] Plot3D[FourierTransform[h[x, y], {x, y}, {k1, k2}], {k1, -5, 5}, {k2, -5, 5}] So I…
lIlIIIllIIIllII
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3 answers

extracting phase from sinusoidal data

I am dealing with data which are essentially are sinusoidal with various degrees of noise. I have an interest in extracting the phase of the data and rather than simply fitting a sine wave, I would like to extract it from the fourier space as there…
alex
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1 answer

How do I make an explicit DFT?

So to gain a better understanding of how Discrete Fourier Transforms are done, I'm trying to program one in Mathematica so I can easily check my answers with the built-in Mathematica code. Based on Wolfram's page on the DFT, I see that I have to sum…
Mumbo
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6
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0 answers

Different FourierParameters in each dimension for discrete Fourier transform

I have a query about the Fourier utility, that does discrete Fourier transforms. I am unable to find any information on whether different FourierParameters can be used in each dimension. This is a natural thing to do in wave theory where you have…
Paul Cally
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6
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2 answers

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 2*Sin[x]. I think they should be somwhere about 2. But…
user12991
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