Questions tagged [fourier-transform]

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85 views

Solving Poisson-like PDE with FFT

Problem I have an $n\times n$ grid, and each point on the grid is assigned two values: a score, and an (inverse) speed factor. There is a "turtle" moving along the grid, and it's goal is to ...
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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
66 views

How to obtain the exact value of wavelength from a 2D FFT amplitude vs wavenumber plot like it is obtainable from 1D FFT amplitude vs wavenumber plot?

I have a two dimensional multi modal spatial signal generated from a MATLAB code using sinusoidal functions of different wave numbers, amplitudes and phases. What I want to know is that if I have 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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1answer
107 views

Reason behind different outputs for Fast Fourier Transform in Numpy and Matlab

Here is the output of Numpy np.fft.ifft([0, 4, 0, 0]) array([ 1.+0.j, 0.+1.j, -1.+0.j, 0.-1.j]) # may vary Here is the output of Matlab ...
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0answers
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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2answers
130 views

The derivative of a gauss function via FFT and IFFT in Python

I have a problem with computing a derivative of a Gauss function using FFT and IFFT from NumPy library. I use the fact that $$ \begin{equation} \frac{d}{dx}f(x) = \frac{1}{\sqrt{2\pi}}\int{ike^{ikx}\...
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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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1answer
869 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 ...
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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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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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2answers
674 views

Computing numeric derivative via FFT - SciPy

I wrote the following code to compute the approximate derivative of a function using FFT: ...
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1answer
149 views

How to define a dimensionless Objective function for determining how peaked a curve is?

I have attached 2 plots for FFT spectra. One is considered good and one is bad. The good one is classified on the basis of how closely spaced the frequencies and the bad is based on how multiple ...
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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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1answer
131 views

Problem implementing convolutions exactly with the FFT

I'm trying to perform convolutions as defined mathematically $f \star g (\tau)= \int_{\mathcal{R}}f(t-\tau)g(t) dt$ in a numerical simulation. Hence, my signal is a sampling of points $f(x_i)$. I ...
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1answer
110 views

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 ...
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0answers
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 ...
4
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1answer
153 views

Computation of triple nested loops as a convolution product?

I'm trying to compute efficiently the following \begin{equation} A_j = \sum_{l'=1}^{\infty}\sum_{k= 0}^{K-1} L_{l'}T_ke^{2\pi i \frac{k}{K}j}\epsilon_{l',k} \end{equation} for $j = 0,1, \ldots, K-2,K-...
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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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0answers
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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2answers
292 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 ...
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0answers
18 views

Normalising DFTs Correctly

I have been playing around with convolutions in scipy's signal package: ...
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1answer
559 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 ...
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0answers
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 ...
4
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1answer
153 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 ...
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0answers
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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1answer
64 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 $|u(k)|=\sqrt{2E(k)}$. ...
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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
141 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 ...
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2answers
434 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 ...
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0answers
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, ...
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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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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}...
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1answer
427 views

Incorporating a potential barrier in a wave-packet simulation (Fourier Transform method)

I'm trying to simulate the scattering of a wave-packet at a potential barrier in Python. I'm using a Fourier Transform method (not sure if its the same as the Split-Step method), where I apply Fourier ...
3
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2answers
129 views

DFT of $g(\omega) \exp(i C \omega^2)$. How to do it ,if uniform sampling requires too much memory?

I have a following problem : I want to transform a function $g(\omega) \exp(i C \omega^2)$. $g(\omega)$ is real and limited. It changes slowly compered to $\exp(i C \omega^2)$. I have a black box that ...
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0answers
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 $-i$?
2
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1answer
60 views

FFT of “implicitly” uniform data

I am trying to take a Fourier transform of a density field estimated from mock galaxy survey catalogs. Basically, you start with a list of galaxy positions, then you bin these positions over some ...
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0answers
98 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 ...
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0answers
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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2answers
131 views

How to solve diffusion equation in Fourier space when mobility is not constant

I want to solve non-classic diffusion equation in Fourier space. The equation is $$∂c/∂t=-∇.J$$ Where $J$ is $$J= -M.∇μ$$ Where M is mobility. It depends on c and $\mu$ is $$ μ= g(c) - \nabla^2c $$ ...
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1answer
391 views

High precision Discrete Fourier Transform in c

I'm trying to do a high precision discrete fourier transform on a signal. To examine the precision, I use a gaussian function as the signal, because the fourier transform is also a gaussian function. ...
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0answers
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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1answer
87 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 ...
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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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0answers
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 ...
0
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1answer
145 views

Hankel transform from paper works only for certain functions

I implemented an algorithm for solving the Hankel transformation based on a paper. My problem is: It works very good for the functions suggested in the paper (as test functions), it works pretty ok ...