# Questions tagged [fourier-analysis]

Questions on the computational aspects of Fourier analysis, including the various applications of the fast Fourier transform (FFT).

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### How to take the Fourier transform of a Fibonacci chain in a Python script?

This may be an easy question to answer but I am really stuck. In several topics (especially that of quasicrystals) the Fibonacci chain's Fourier transform and diffraction pattern is mentioned. Despite ...
1 vote
138 views

### Deconvolution of sinc function in spectrum calculation in FTS

In Fourier transform spectroscopy (FTS) I am calculating a broadband interferogram (e.m. frequency 190-300 GHz top-hat), then back-retrieving the spectrum by FT. Here in the figure, you can see the ...
41 views

### Describing a vector field

I am currently making use of a 2D vector field that I would like to be able to describe and characterize. I thought of a few metrics that I could use, but they seem limited for both a qualitative and ...
1 vote
56 views

### How do people deal with resized grid steps while numerically integrating using discrete Fourier Transform?

I am trying to simulate light propagation on python using FFT following the Fresnel diffraction equation given on Wikipedia: The problem with this is that the output matrix from the DFT would be ...
74 views

1 vote
6k views

### Understanding why scipy.fft.fft (fast Fourier transform) doesn't work as expected

I write the following fast Fourier transform code into my Python notebook expecting to see a plot wherein there's a spike at $1/2\pi$ since that's the frequency of the sin function, but instead I get ... 106 views

### Cauchy Lorentzian simulation on FFT with oscillation

Recently I do simulation on Lorentzian Function with FFT Lorentzian Function is 2a/(x**2+a**2) ...
68 views

1 vote
883 views

### Numpy FFT gives me a pulse shorter than it should be. Not sure what I am doing wrong

I've created a code (Python, numpy) that defines an ultrashort laser pulse in the frequency domain (pulse duration should be 4 fs), but when I perform the Fourier Transform using DFT, my pulse in the ...
1 vote
131 views

### Demagnetizing field using scalar potential method

I want to calculate the stray magnetic field from a ferromagnet using the scalar potential method (1). The problem consists of a ferromagnetic cuboid divided into small cuboidal cells in which the ...
221 views

117 views

### FFTW on subarray with MPI

With the guru interfaces of FFTW, I can apply transforms only to parts of a multidimensional array by modifying the fftw_iodim ...
1 vote
38 views

### How to numerically transform a 2D Fourier spectrum with arbitrary frequency shift to center frequency?

Suppose $F(u,v)$ is the center frequency Fourier representation of some $f(x,y)$ in 2D. $$f(x,y)=\int\limits_{-\infty}^{\infty}\int\limits_{-\infty}^{\infty}F(u,v)e^{2\pi i (xu+yv)}dudv$$ In ...
147 views

### Discrete sine and cosine transform for mixed derivatives

Using sine and cosine transforms to solve Poisson's equation with Dirichlet boundary conditions seem quite standard nowadays (see, e.g., here or Table 2 in this paper). In the case of Poisson's ...
4k views

### Error propagation through an FFT

If I take the Fourier transform of data $x \pm \sigma$, is there a standard approach to what the error in the outputs will be? Would the best way be a direct evaluation of the upper and lower bounds?
1 vote
295 views

### Fourier transform spherical system

I need to take the Fourier transform of a 3D function $h(r)=h(|r|)$ so that I can invert a convolution problem. What is the best way to do this with Python? I know the the FT is equivalent to a sine ...
1 vote
122 views

### Code for solving the heat equation on the semi-infinite rod

Cross posted in mathematica.SE. Question : I want to test the solution which is given below is right by Matlab/Maple/Mathematica. Please look the post in mathstackexhange or Please look below. ...
232 views

1 vote
116 views

### fft with non uneven spacing between the value of the signal

I am trying to implement in C or C++ a solution for a fft and Ifft when the signal values are not obtained at a constant rate, making it having a desviation between the values and the periodic ones. I ...
1k views

### 1-D turbulent energy spectra in homogeneous direction (non-isotropic)

I am trying to compute the one-dimensional energy spectra for my channel-flow simulation. I have already written a post-processing script to achieve this; however, I need to validate my code before ...
1 vote
76 views

### Perfect filtering of high frequencies in 2D FFT (Multidimensional 2/3 Rule)

Let $u_n$ be an array containing discrete values of the function $u(x,y)$. Performing a 2D FFT to this array we obtain $\hat{u_n}$ representing the values of $\hat{u}(k_x,k_y)$. I would like to ...
### How to do numerical computation of $L^p$ norm of a $p$ dimensional trigonometric polynomial
Id like to know methods for numerical computation of $L^2$ norm of a two dimensional trigonometric polynomial. I have the coefficients. If I want to compute the L^1 norm, I can do so by sampling in ...