# Questions tagged [fourier-transform]

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

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### 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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### 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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### 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 ...
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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)=\... 3 votes 2 answers 475 views ### Chebyshev differentiation via FFT with a domain [a,b] I want to ask something about Chebyshev differentiation via FFT, which can be used to obtain with spectral accuracy the derivative of a smooth function. See for instance this code in python, which ... 2 votes 0 answers 18 views ### Normalising DFTs Correctly I have been playing around with convolutions in scipy's signal package: ... 4 votes 1 answer 719 views ### How to use matlab command 'fft' to solve Ax=b arising from Poisson equation? I want to ask a question about fast solver to the Poisson equation with Homogenous boundary conditions as follows: $$-\Delta u = f.$$ After centered difference using$n+2equidistance points in all ... 0 votes 0 answers 111 views ### Smoothing FFT result I am trying to calculate the spectrum of Bremmstrahlung, which involves calculating the Fourier transformed acceleration. I am solving a non-linear ODE to numerically calculate the acceleration in the ... 4 votes 1 answer 174 views ### Differences between Discrete Fourier Transform and Continuous Fourier Transform? I am trying to visualize the time dependence of a free particle given an initial wave-function using Python and I just wanted to know if I could use the in built FFT implementation from NumPy to find ... 2 votes 0 answers 30 views ### Palmprint Identification - Why do we align the images before we use the Fourier Transform? I am currently reading the paper PALMPRINT IDENTIFICATION BY FOURIER TRANSFORM by WENXIN LI, DAVID ZHANG and ZHUOQUN XU about identifying persons based on an image of their palm, one version of the ... 1 vote 1 answer 70 views ### Obtain velocity from imposed energy spectrum using the inverse FFT I am trying to obtain the spatial representation ofu(x)$(e.g. velocity) from its energy spectrum$E(k)=k^4\exp(-(k/k_0)^2)$, which is given in the frequency domain, provided$|u(k)|=\sqrt{2E(k)}$. ... 2 votes 0 answers 87 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 ... 3 votes 1 answer 172 views ### Calculating the Convolution Using DFT (FFT) I have the following convolution as part of a numerical simulation. $$T(r)=\int \mathrm{d}^3r_2\, p(r_2)f(r_2)\alpha(r-r_2)\, .$$ My problem is that the analytical expressions for$f$and$p$do ... 1 vote 2 answers 622 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 ... 0 votes 0 answers 31 views ### 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, ... 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 ... 0 votes 1 answer 146 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}... 