Questions tagged [fourier-transform]
For questions about Fourier transforms, how they are used, and implementation details.
97
questions
-2
votes
0answers
23 views
Aeroacoustics Simulation in Star CCM+ using FW-H Model
Trying to simulate the aeroacoustics noise generation due to a flow over a open cavity using Broadband Noise Model and also noise propagation in the far field using FW-H Model.
The Star CCM user guide ...
3
votes
1answer
37 views
Bounds condition for IFT to obtain a $1/f$ time-series
I am coding a function to obtain a randomized time-series from a given $\frac{1}{f}$ law.
The randomization is obtained by introducing a random phase in the function.
I experience a problem in the ...
0
votes
0answers
30 views
Gridline cutouts after FFT and iFFT on Python
EDIT: I think I messed up on the coordinates of $(p,q)$. Num was missing a multiple of $2\pi/N$. Assuming my interpretation of DFT isn't wrong.
I am currently using FFT to run Fresnel Diffraction as ...
0
votes
0answers
22 views
Fast nonuniform DFT works for complex frequencies (damping), more or less. How to improve?
A variety of algorithms for the fast evaluation of the nonuniform DFT is available, both in theory, and in libraries like
NFFT3
NUFFT
FINUFFT
I need to evaluate $a_k=\sum_{j=0}^{m-1} A_j \exp(2\pi i ...
1
vote
0answers
52 views
How do people deal with resized grid steps while numerically integrating using discrete Fourier Transform?
I am trying to simulate light propagation on python using FFT following the Fresnel diffraction equation given on Wikipedia:
The problem with this is that the output matrix from the DFT would be ...
1
vote
0answers
36 views
How do you correctly implement Scipy's FFT procedures to produce a low-pass filter - image processing
I'm following this low-pass filter example in the text "Image Operators: Image Processing in Python 1st Edition" by Jason M. Kinser, but can't seem to duplicate their results.
The text's ...
3
votes
0answers
40 views
3D Cooley-Tukey FFT
To compute the $N$-point DFT
$$ X[k] = \sum_{n=0}^{N-1} x[n] W_N^{kn} $$
where $N = N_1 N_2$, we can write the indices as $n = N_2 n_1 + n_2$ and $k = k_1 + N_1 k_2$, (effectively packing the data ...
1
vote
0answers
37 views
2D DFT for lower frequencies only; is there something significantly faster than numpy.fft.fft2 (throwing away high frequencies)?
I do a lot of 2D discrete FFT in python using np.fft.fftshift(np.fft.fft2(y)), then throw away 90% or more of the array, keeping only the central low-frequency area....
1
vote
0answers
109 views
Fast evaluation of trigonometric polynomials
Suppose you have a trigonometric polynomial of the form
\begin{equation*}
x(t) = \sum_{k = 0}^N a_k \cos(2 \pi k f_0 t).
\end{equation*}
Using Clenshaw algorithm, one can evaluate this polynomial in $...
2
votes
1answer
97 views
1
vote
1answer
121 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 ...
0
votes
0answers
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 ...
-1
votes
1answer
127 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 ...
1
vote
1answer
82 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 ...
1
vote
1answer
240 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
...
1
vote
0answers
45 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. ...
1
vote
2answers
217 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
$$
\begin{equation}
\frac{d}{dx}f(x) = \frac{1}{\sqrt{2\pi}}\int{ike^{ikx}\...
1
vote
1answer
2k views
Understanding why scipy.fft.fft (fast Fourier transform) doesn't work as expected
I write the following fast Fourier transform code into my Python notebook expecting to see a plot wherein there's a spike at $1/2\pi$ since that's the frequency of the sin function, but instead I get ...
0
votes
0answers
366 views
How to take convolution of two arrays in Python by using NumPy?
Generally, we know that if we have this relation between Fourier transforms of three functions in frequency domain as:
$$\mathfrak{F}\{\mathsf{P}(t)\} = \mathfrak{F}\{\mathsf{Z}(t)\}\mathfrak{F}\{\...
1
vote
0answers
67 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 ...
4
votes
2answers
1k views
Computing numeric derivative via FFT - SciPy
I wrote the following code to compute the approximate derivative of a function using FFT:
...
4
votes
1answer
164 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 ...
1
vote
0answers
35 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,...
3
votes
1answer
167 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 ...
2
votes
1answer
114 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 ...
1
vote
0answers
56 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
votes
1answer
158 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-...
1
vote
0answers
42 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 ...
1
vote
0answers
56 views
1
vote
0answers
117 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
387 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
0answers
18 views
Normalising DFTs Correctly
I have been playing around with convolutions in scipy's signal package:
...
4
votes
1answer
647 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.$$
After centered difference using $n+2$ equidistance points in all ...
0
votes
0answers
106 views
Smoothing FFT result
I am trying to calculate the spectrum of Bremmstrahlung, which involves calculating the Fourier transformed acceleration. I am solving a non-linear ODE to numerically calculate the acceleration in the ...
4
votes
1answer
166 views
Differences between Discrete Fourier Transform and Continuous Fourier Transform?
I am trying to visualize the time dependence of a free particle given an initial wave-function using Python and I just wanted to know if I could use the in built FFT implementation from NumPy to find ...
2
votes
0answers
30 views
Palmprint Identification - Why do we align the images before we use the Fourier Transform?
I am currently reading the paper PALMPRINT IDENTIFICATION BY FOURIER TRANSFORM by WENXIN LI, DAVID ZHANG and ZHUOQUN XU about identifying persons based on an image of their palm, one version of the ...
1
vote
1answer
65 views
Obtain velocity from imposed energy spectrum using the inverse FFT
I am trying to obtain the spatial representation of $u(x)$ (e.g. velocity) from its energy spectrum $E(k)=k^4\exp(-(k/k_0)^2)$, which is given in the frequency domain, provided $|u(k)|=\sqrt{2E(k)}$. ...
2
votes
0answers
71 views
Fusing callbacks with FFTs: an open-source GPU FFT implementation?
I'm using cuFFT to do some 2D FFTs on matrices of size 2048x2048 or larger. The FFTs are preceded and followed by various scaling operations.
These scaling operations are memory-bound, so they take ...
3
votes
1answer
158 views
Calculating the Convolution Using DFT (FFT)
I have the following convolution as part of a numerical simulation.
$$T(r)=\int \mathrm{d}^3r_2\, p(r_2)f(r_2)\alpha(r-r_2)\, .$$
My problem is that the analytical expressions for $f$ and $p$ do ...
1
vote
2answers
524 views
Numpy FFT gives me a pulse shorter than it should be. Not sure what I am doing wrong
I've created a code (Python, numpy) that defines an ultrashort laser pulse in the frequency domain (pulse duration should be 4 fs), but when I perform the Fourier Transform using DFT, my pulse in the ...
0
votes
0answers
31 views
Simulating Anderson model, have problem with momentum representation (MATLAB)
I want to change from real-space representation to momentum-space representation I have a Hamilton-operator (Anderson-model), and I calculated some kind of entropy of its eigenstates (this is working, ...
1
vote
1answer
1k views
Split-step Fourier method applied on Schrodinger equation
I'm trying to solve a Schrodinger equation of the form $i\frac{\partial}{\partial t}\psi=-\frac{\partial^2}{\partial x^2}\psi + (V(x)+\alpha|\psi|^2)\psi$ using the split-step Fourier method ...
0
votes
1answer
127 views
Specifying mesh spacing for DFT in numpy
I was testing the .fft package of numpy 1.16.1 in Python 3.7.2. In particular I was trying to verify that the transform resembles the analytical one for: $$f(x) = \mathrm{exp}\left[-\left(\frac{x-5}{2}...
2
votes
1answer
466 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
134 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
vote
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
votes
1answer
66 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 ...
