Questions tagged [fourier-transform]

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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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1answer
738 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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332 views

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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18 views

Normalising DFTs Correctly

I have been playing around with convolutions in scipy's signal package: ...
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29 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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0answers
214 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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0answers
44 views

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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0answers
662 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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41 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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0answers
59 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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0answers
34 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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51 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 ...
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37 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 ...
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41 views
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85 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)=\...
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0answers
59 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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1answer
1k 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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48 views

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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33 views

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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100 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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0answers
81 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 ...
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53 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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82 views

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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602 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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0answers
236 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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16 views

Reducing the frequency resolution for a short pulse by applying the SVEA - how to keep frequency?

If I have a single light pulse, I can define it as (within certain boundaries, and $A$ a gaussian function) $$E(t) = A(t)\cdot\exp(-i\omega_0 t)$$ After applying an FFT over it, I can then shift the ...
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1answer
60 views

Improving efficiency of FFT for large time window and single frequency pulses

Spectral methods for pulse propagation usually require at least one FFT and one iFFT for each step. In my case I have a two-dimensional radially symmetric electric field (one dimension in space, one ...
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0answers
20 views

Temporal/spectral conversion for large fields - best approach?

I am currently working on a more efficient implementation of a pulse propagation algorithm. The propagation is done in the spectral domain, but several evaluations (such as energy calculations) are ...
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0answers
268 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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105 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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26 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, ...
0
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1answer
92 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}...