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### Why Fourier transform is symmetric no matter what interval I choose? [duplicate]

I'm solving a vibration problem. After solving two systems of ODEs (one valid in 0-0.1 and the other in 0.1-1) I get the plot of 3 functions, one of them is this, the plot of the variable $y_w$ (Image ...
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### Fourier FFT frequencies [duplicate]

I am using FFT (Fourier) on a dataset that contains the temperature along a rod 1m long. The data is sampled with a spacing of <...
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1 vote
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### 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 ...
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### How to do the Fourier transform of a picture? [duplicate]

I want to generate Fourier transforms of a picture. the transform can represent the diffraction pattern of the picture. Basically, if I have a picture. Then, the result should look like this: For a ...
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21k 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 ...
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20k 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 ...
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### What's wrong with this FFT-based Von Kármán vortex street simulation?

About 9 years ago, I came across this interesting website, and found the following paragraph with a broken Mathematica code sample: When fluid passes an object, it can leave a trail of vortices ...
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3k 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: ...
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### How can I use fast Fourier transform (FFT) to solve a PDE (heat equation)?

I'm trying to solve a one-dimensional heat equation (PDE) with the Fourier transform numerically, in the way it was done here. The equation: , is subject to the initial condition: , where U(x,t) is ...
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### 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: <...
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### 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, ...
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### Differences between FFT and analytical Fourier Transform

In MATLAB, if I perform an FFT on a simple Gaussian spot with a phase grating: ...
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### Convert MATLAB code solving 1D wave equation via FFT using ode45 into Mathematica code

I don't quite understand the process of solving differential equations by MATLAB. It seems that it doesn't need the explicit function to specify the required solution, but only needs to input the ...
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### Discrete Fourier Transform with x axis data?

Usually, Fourier Transform in mathematica is supplied by y data only, like the famous Sin[x] transform example. What if my data is a list of ...
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