Questions tagged [fourier-transform]

For questions about Fourier transforms, how they are used, and implementation details.

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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 ...
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1 answer
851 views

Help with Fourier beam propagation method

I am working on implementing the Fourier beam propagation method in C++. I am really more of a programmer than a physicist but I think I have a good understanding of what I am trying to do. Here is ...
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3D Cooley-Tukey FFT

To compute the $N$-point DFT $$ X[k] = \sum_{n=0}^{N-1} x[n] W_N^{kn} $$ where $N = N_1 N_2$, we can write the indices as $n = N_2 n_1 + n_2$ and $k = k_1 + N_1 k_2$, (effectively packing the data ...
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How to obtain values in physical space for a given spectrum?

My question falls under purview of turbulent flows. I want to add an initial perturbation, for which I have a given energy spectrum (say$ E(k)=ak^4e^{-bk^2} $). The steps involved in getting these ...
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Normalising DFTs Correctly

I have been playing around with convolutions in scipy's signal package: ...
2 votes
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30 views

Palmprint Identification - Why do we align the images before we use the Fourier Transform?

I am currently reading the paper PALMPRINT IDENTIFICATION BY FOURIER TRANSFORM by WENXIN LI, DAVID ZHANG and ZHUOQUN XU about identifying persons based on an image of their palm, one version of the ...
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99 views

Fusing callbacks with FFTs: an open-source GPU FFT implementation?

I'm using cuFFT to do some 2D FFTs on matrices of size 2048x2048 or larger. The FFTs are preceded and followed by various scaling operations. These scaling operations are memory-bound, so they take ...
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2 votes
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236 views

Solving a 3D (almost radial) convolution with FFT

I have a 3D integral that is almost a radial convolution of the form $$ \int d^{3}k'h(\mathbf{k'})g(|\mathbf{k-k'}|) $$ and I am looking for a fast and efficient algorithm (e.g. FFT) to solve it ...
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Constructing 2 fold oversampled cosine basis in MATLAB

So I'm trying to construct a 2 fold oversampled cosine basis in MATLAB. I know how to construct the basis as a square matrix using the following command: ...
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2 votes
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827 views

Fast Forward Laplace transform

There are examples for fast numerical inversion of the Laplace transforms. For example here: http://www.mathworks.com/matlabcentral/fileexchange/32824-numerical-inversion-of-laplace-transforms-in-...
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29 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 ...
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1 vote
1 answer
136 views

How to perform FFT from plane-wave basis function coefficients to real space?

I have a 3D grid in real space of grid spacing $L$ and say 21 grid points in each direction, containing e.g. a charge distribution. This is stored as a numpy array of shape ...
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53 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 ...
1 vote
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60 views

How do you correctly implement Scipy's FFT procedures to produce a low-pass filter - image processing

I'm following this low-pass filter example in the text "Image Operators: Image Processing in Python 1st Edition" by Jason M. Kinser, but can't seem to duplicate their results. The text's ...
1 vote
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119 views

Fast evaluation of trigonometric polynomials

Suppose you have a trigonometric polynomial of the form \begin{equation*} x(t) = \sum_{k = 0}^N a_k \cos(2 \pi k f_0 t). \end{equation*} Using Clenshaw algorithm, one can evaluate this polynomial in $...
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54 views

Fourier transform in finite element

I have a finite element solver where I am using tetrahedral elements. I am solving for electric potentials and then calculate the current densities in each element, which are constant in each element. ...
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71 views

Problems with simulation of a spatial filter 4f setup (Python)

I have a question about my code which computes numerically the output field of a 4f setup with a pinhole in the middle which works as a spatial filter. My setup consists of two lenses with 50mm focal ...
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35 views

Solving a spectral system by reducing it to a single frequency - Feasability of approach?

I'm trying to solve the linear non-paraxial pulse propagation equation $$\partial_z\hat{E}=ik_z\hat{E}$$ for a field defined as $$E=E(r, t, z)$$ The equation given above uses $$\hat{E}=\hat{E}(k_\perp,...
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Advantage of fractional Fourier transform over multiscale wavelet?

What could be the arguments of using fractional Fourier transform instead of multiscale wavelet for data analysis ? Optimization of the good time-frequency domain parameter? good in the sens of best ...
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44 views

FFT convolution works only with certain domain length

in my quest to understand how I can use FFT to compute integrals (see my other question click, still no answer there), I came across the fact that a convolution of two functions can be calculated by ...
1 vote
0 answers
74 views

How do I calculate the amplitude after a 2D r2c transform using FFTW?

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147 views

Calculate integrals using numpy.fft

Good evening, I would like to understand why I do not get the correct result: I assume that I know my function on discrete data points and expand it as a discrete Fourier transform: $\text{sin}(x)=\...
1 vote
1 answer
2k views

Split-step Fourier method applied on Schrodinger equation

I'm trying to solve a Schrodinger equation of the form $i\frac{\partial}{\partial t}\psi=-\frac{\partial^2}{\partial x^2}\psi + (V(x)+\alpha|\psi|^2)\psi$ using the split-step Fourier method ...
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The sign of Schrodinger equation

I have a question for the format of Schrodinger equation $$\psi(x,t) = \int_0^\infty c_n e^{-iE_nt/\hbar} \psi_n(x)$$ Why do we have $i$ instead of $-i$?
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What is the inverse Laplace transform algorithm that is most accurate given the fewest frequencies considered?

Based on your empirical knowledge. This paper suggests a nonlinearly accelerated Fourier series approach, such as the one proposed here, but I have one constraint: we should be able to express the ...
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106 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. ...
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83 views

Can x-ray back-projection be converted to hard-field magnetic induction tomography?

This is a question about hard-field back-projection as used in x-ray tomography, applied magnetic induction tomography. Al-Zeibak and Saunders have shown that x-ray filtered backprojection can be ...
1 vote
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57 views

Beam propagation over extremely short distances

I like to simulate the free-space propagation of an electric field (beam radius ~ 1-10 cm) over extremely short distances (~ 5-10 cm). The reason is that the field is focused by a lens with a very ...
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Spherical Harmonics: band-limited representations of a vector field on a sphere

I have used pyShtools in the past to expand scalar functions to spherical harmonics and to synthesize band-limited representations of them. However, I am not too sure how to achieve this for a vector ...
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702 views

3D plot from Fourier coefficients in Matlab

I would like to construct a surface on a 2D mesh, given a set of Fourier coefficients for the original function $V(x,y)$. Given some $\mathbb{K}\subset \mathbb{Z}^2$ I have a partial double sum of a ...
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266 views

Am I using the incorrect implementation of the fast Chebyshev transform?

I was told that the fast Chebyshev transform has superior spectral convergence, but I am unable to verify its rumored convergence. I was given plots of its spectral convergence, where the signal's ...
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Error when taking the continuous time Fourier transform

I am trying to figure out what the error is associated with taking a Fourier transform, using Matlab. I have a 1D vector A of 130 elements and I know the error ...
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41 views

Gridline cutouts after FFT and iFFT on Python

EDIT: I think I messed up on the coordinates of $(p,q)$. Num was missing a multiple of $2\pi/N$. Assuming my interpretation of DFT isn't wrong. I am currently using FFT to run Fresnel Diffraction as ...
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30 views

Fast nonuniform DFT works for complex frequencies (damping), more or less. How to improve?

A variety of algorithms for the fast evaluation of the nonuniform DFT is available, both in theory, and in libraries like NFFT3 NUFFT FINUFFT I need to evaluate $a_k=\sum_{j=0}^{m-1} A_j \exp(2\pi i ...
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416 views

How to take convolution of two arrays in Python by using NumPy?

Generally, we know that if we have this relation between Fourier transforms of three functions in frequency domain as: $$\mathfrak{F}\{\mathsf{P}(t)\} = \mathfrak{F}\{\mathsf{Z}(t)\}\mathfrak{F}\{\...
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112 views

Smoothing FFT result

I am trying to calculate the spectrum of Bremmstrahlung, which involves calculating the Fourier transformed acceleration. I am solving a non-linear ODE to numerically calculate the acceleration in the ...
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Simulating Anderson model, have problem with momentum representation (MATLAB)

I want to change from real-space representation to momentum-space representation I have a Hamilton-operator (Anderson-model), and I calculated some kind of entropy of its eigenstates (this is working, ...
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1 answer
165 views

Specifying mesh spacing for DFT in numpy

I was testing the .fft package of numpy 1.16.1 in Python 3.7.2. In particular I was trying to verify that the transform resembles the analytical one for: $$f(x) = \mathrm{exp}\left[-\left(\frac{x-5}{2}...
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