# Questions tagged [fourier-transform]

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### Fourier spectral method for coordinate transformed heat equation

As the title said, I want to solve a coordinate transformed heat equation using fourier spectral method. In particular, I am interested in transforming an uniform grid into an adaptive non-uniform ...
27 views

### Why am I not getting the flat phase when Fourier-transform a Fourier-limited Gaussian pulse?

I have been trying to obtain a spectrum and a spectral phase of a Gaussian pulse using the Fast Fourier Transform provided with numpy library in Python. Here are ...
42 views

### 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 ...
39 views

### Propagation of a Gaussian beam using FFT

I am trying to simulate the propagation of a gaussian beam through a lens using an FFT approach. I tried to implement the approach described by Couairon in this paper at page 43: https://link....
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### 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 ...
18 views

### Normalising DFTs Correctly

I have been playing around with convolutions in scipy's signal package: ...
132 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 $n+2$ equidistance points in all ...
70 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 ...
86 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 ...
28 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 ...
49 views

### Obtain velocity from imposed energy spectrum using the inverse FFT

I am trying to obtain the spatial representation of $u(x)$ (e.g. velocity) from its energy spectrum $E(k)=k^4\exp(-(k/k_0)^2)$, which is given in the frequency domain, provided $|u(k)|=\sqrt{2E(k)}$. ...
40 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 ...
89 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 ...
179 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 ...
23 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, ...
352 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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### 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 ...
246 views

### MPI support for discrete Fourier transform (DFT) in Python

I am looking for a discrete Fourier transform (DFT) library that can be run with MPI on Python. Usually, in other languages (C, Fortran) FFTW is used. There's a Python wrapper for FFTW called pyFFTW, ...
145 views

### Approximating improper integral with FFT

In d'Halluin et al. (2005) (http://imajna.oxfordjournals.org/content/25/1/87.short) the authors claim that the correlation integral $$I(x) = \int_{-\infty}^{\infty} V(x+y) f(y) dy$$ can be ...
203 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 ...
202 views

### Amplitude at a given frequency in a wide band signal

Could anyone suggest the most computationally efficient method for finding amplitude at a given frequency having a noisy wide band signal. To be more specific about a task. I have some physical ...