Questions tagged [fourier-transform]
The fourier-transform tag has no usage guidance.
71
questions
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11 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....
4
votes
1answer
110 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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0answers
36 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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67 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)=\...
3
votes
2answers
87 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
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0answers
18 views
Normalising DFTs Correctly
I have been playing around with convolutions in scipy's signal package:
...
3
votes
1answer
100 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 ...
0
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0answers
67 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 ...
3
votes
1answer
62 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
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0answers
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 ...
1
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1answer
46 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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37 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
1answer
84 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
1answer
148 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
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, ...
0
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1answer
201 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
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1answer
35 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: $$f(x) = \mathrm{exp}\left[-\left(\frac{x-5}{2}...
2
votes
1answer
132 views
Incorporating a potential barrier in a wave-packet simulation (Fourier Transform method)
I'm trying to simulate the scattering of a wave-packet at a potential barrier in Python. I'm using a Fourier Transform method (not sure if its the same as the Split-Step method), where I apply Fourier ...
3
votes
2answers
120 views
DFT of $g(\omega) \exp(i C \omega^2)$. How to do it ,if uniform sampling requires too much memory?
I have a following problem : I want to transform a function $g(\omega) \exp(i C \omega^2)$. $g(\omega)$ is real and limited. It changes slowly compered to $\exp(i C \omega^2)$. I have a black box that ...
1
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0answers
46 views
The sign of Schrodinger equation
I have a question for the format of Schrodinger equation
$$\psi(x,t) = \int_0^\infty c_n e^{-iE_nt/\hbar} \psi_n(x)$$
Why do we have $i$ instead of $-i$?
2
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1answer
55 views
FFT of “implicitly” uniform data
I am trying to take a Fourier transform of a density field estimated from mock galaxy survey catalogs.
Basically, you start with a list of galaxy positions, then you bin these positions over some ...
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0answers
70 views
Discrete sine and cosine transform for mixed derivatives
Using sine and cosine transforms to solve Poisson's equation with Dirichlet boundary conditions seem quite standard nowadays (see, e.g., here or Table 2 in this paper). In the case of Poisson's ...
1
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0answers
32 views
What is the inverse Laplace transform algorithm that is most accurate given the fewest frequencies considered?
Based on your empirical knowledge.
This paper suggests a nonlinearly accelerated Fourier series approach, such as the one proposed here, but I have one constraint: we should be able to express the ...
0
votes
2answers
111 views
How to solve diffusion equation in Fourier space when mobility is not constant
I want to solve non-classic diffusion equation in Fourier space. The equation is $$∂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 $$ ...
0
votes
1answer
286 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
90 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.
...
1
vote
1answer
68 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 ...
1
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0answers
76 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
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0answers
51 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
votes
1answer
140 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 ...
1
vote
1answer
238 views
Power spectrum incorrectly yielding negative values
I have a real signal in time given by:
And I am simply trying to compute its power spectrum, which is the Fourier transform of the autocorrelation of the signal, and is also a purely real and ...
3
votes
2answers
1k views
Fourier transform by FFT : by using cubic splines to interpolate between data points, do we change the frequency content of the Fourier transform?
I have a data file with some points equally spaced. These represent some function. I have to calculate the Fourier transform of this set of points. The thing is, I'm tempted to take a cubic spline of ...
0
votes
1answer
79 views
0 Hz (quite sharp) peak in FFT and division by 0
In a previous question, link, I asked about how I could most effectively do a Fourier Transform of a radial function given at certain values and which we knew the asymptotical behaviour of. The ...
3
votes
1answer
1k views
Fast(er) computation of dot product of two convolutions?
Let $a,b,c,d\in\mathbb{R}^n$. Is it possible to compute
$$\langle a*b,c*d\rangle$$
faster than 6 FFTs?
I can do it with 6 FFTs by doing normal convolutions, 3 FFTs each.
In my application I know $b, ...
3
votes
2answers
318 views
How to calculate efficiently and accurately the Fourier transform of a radial function in Fortran
As my question states, I want to calculate the Fourier transform $F(q)$ of a radial function $f(r)$ (defined on $[0,\infty)$ and which decays like an exponential $\exp(-Ar+b)$ at large $r$) as ...
0
votes
2answers
266 views
Generating initial velocity field
I am trying to generate initial velocity field which satisfies incompressible flows condition. To formulate this I am using Rogallo's procedure formulation which is given by
$$
\tilde{u}(k) = \frac{\...
1
vote
0answers
73 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 ...
3
votes
1answer
241 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, ...
2
votes
1answer
143 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 ...
2
votes
0answers
197 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 ...
2
votes
3answers
196 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 ...
6
votes
2answers
11k views
C++ libraries for Fast Fourier Transform in high precision
I am looking for a C++ library for Fast Fourier Transform (FFT) in high precision (e.g., using high precision real data types similar to mpfr_t in MPFR or ...
2
votes
1answer
295 views
How do I avoid divide-by-zero when solving the Poisson equation with Fourier transforms?
I wanted to try to implement part of the method in the following article using Fourier transforms.
http://www.shodor.org/media/content/jocse/student_submissions/nocito2010/nocito2010_pdf
Right now I ...
2
votes
1answer
695 views
Numerically computing the advection equation
I am trying to write a program to compute the advection equation.
$$u_t +u_x = 0$$
I use the spectral method for the spatial derivative $u_x$ and the leapfrog method for the time derivative $u_t$.
...
4
votes
1answer
579 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 ...
3
votes
0answers
287 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 ...
