Questions tagged [fourier-analysis]
Questions on the discrete and continuous Fourier analysis functions of Mathematica, as well as the FourierSeries` package.
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Plotting the energy density of Gravitational Waves
Is there a way to reproduce the curve of the spectral energy density of the Gravitational Waves in Mathematica, Figure (1) in : 0703290. It is given by Equations (63) and (64).
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Table of integrals involving modified Bessel function of the second kind
I need to compute integrals of the following form as accurately as possible (possibly with extended precision):
$$
I_{nl}(\omega)=\int_0^{1/2}\left(1-x^2\right)^{1/4} \sin (2 \pi l x)\; \sin (2 \pi ...
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Why don't my Fourier series coefficients match with the output of the Discrete Fourier Transform (DFT)?
The question I am about to ask should be more inclined towards a mathematical problem rather than Mathematica's syntax or application issues. However, I try to ask here first because I have received a ...
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How to use Mathematica for demonstration of Analysis of Boolean functions?
I am wondering how to use Mathematica to demonstrate some concepts in Analysis of Boolean functions, e.g.:
Influence
Noise stability
Noise operator
$L_q$-norm and $L_\infty$ norm of a boolean ...
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Inversion in Fourier coefficients estimation problems
Let us suppose we have a coefficient vetor:
coeff = {a0, a1, b1, a2, b2, ..., an, bn}
with a total of (2*n + 1) elements. Those coefficients are applied in a ...
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1
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Apply a function to a list of data
Im basically messing around with discrete Fourier-Transformation and I cant figure out how to apply it. I know there exists a predefined command, but I want to learn the computation behind it and im ...
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Calculate Fourier coefficients in optimization problem [closed]
I am using Differential Evolution optimization algorithm to estimate Fourier Coefficients to recover my objective function. In this case, coefficient samples are generated, and then the algorithm ...
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1
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Compute Fourier Series from Fourier Transform
I am trying to get the coefficients of the classical Fourier Series from Mathematica's Fourier Transform.
Now as I understand, Mathematica provides the Fourier Series coefficients:
...
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FourierTransform bug
I have been having some issues with FourierTransform in Mathematica 13.1 which I believe boil down to this simple example.
Consider the Fourier transform of the function ...
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1
answer
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Fourier Transform of a Piecewise Function [closed]
I'm trying to do the Fourier Transform of the function below
Where R is just a constant, and I would like to transform from x into k space and here is my code:
...
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Implement the constant-Q transform in a custom audio encoder
I'm working on a project in Wolfram Language where I need to implement the Constant Q Transform (CQT) in a custom audio encoder. The CQT is a time-frequency analysis method that is often used in music ...
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Demonstration of Fourier Series: Selectable Target Function, Selectable Number of Coefficients, Scrolling Graph
There are a number of nice Wolfram Demonstrations on Fourier Series, but none quite what I seek. The closest I've found is this one, but it has several unnecessary features (e.g., colors) and missing ...
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A Fourier transform that skips dimension
I have a [29990, 1, 512, 1] dimension list. I want to do Fourier transform over all [ -- , 1,512,1] and skip the first dimension. I appreciate it if you could help me.
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How to calculate a numerical Fourier transform obtained from NDSolve?
We numerically solve for the electric potential on a box which obeys Ohm's law:
\begin{equation}\nabla\cdot(\overset{\scriptscriptstyle\leftrightarrow}{\sigma} \nabla \Phi) = 0, \label{Eqn:OhmsLaw}\...
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InverseFourierSinTransform on Mathematica did not give a result
I am trying to solve the linear Schrödinger equation with the Fourier transform. I have difficulty making the corresponding graph when I solve the problem numerically. Can you explain to me what is my ...
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Difficulty to create the 3D plot of the Linear Schrödinger equation (Fourier Transform)
I am trying to solve the linear Schrödinger equation with Fourier transform as follows. Although analytically I was able to solve it and create the graphs I wanted. I have difficulty making the ...
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How to get DFT from Sound/Audio/Image?
When I'm trying to do Discrete Fourier Transform or just get a ListPlot of values from Sound object, I get error message..
I understand that Fourier command (and ListPlot of course) works only with ...
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Why does FourierSequenceTransform of Cosine result in amplitude of 1/2?
Can anyone explain why my results with FourierSequenceTransform differ from the values in a table in my textbook?
The definition of Discrete-Time Fourier Transform (...
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Fourier neural operator using wolfram mathematica
Fourier Neural Operator (FNO) is a neural network-based approach that combines deep learning with the Fourier transform to solve partial differential equations. It leverages the power of neural ...
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InverseFourier, Time response from the pressure over frequency
the problem I'm trying to solve is much more involved, that is I'm trying to get the Time Response for an Impulse Input for a loudspeaker starting from the pressure it generates over the frequency:.
...
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What are the correct FourierParameters for this computation?
Similar to this question on Math StackExchange, I'd like to show that the Fourier transform of a Gaussian is the same function. Specifically, I'd like to use Mathematica's ...
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Obtaining better Fourier series for a piecewise constant function
I have the give wave-train:
and I extract the given set of points:
...
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61
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Fourier Transformation over 30000 .h5 files
I have 30k .h5 files and need to do a Fourier transformation over one specific data set in each file. Then I need to put them on a list.
Ultimately, I need a list of all Fourier transformations of ...
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InverseFourierCosTransform
As a following one of my previous question, I have a function about Z and take an InverseFourierTransform of it as:
...
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FourierCosTransform [duplicate]
I have a question related to "FourierCosTransform" command in Mathematica. I have tested the following codes:
...
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Problem in Comoressing Image using Fourier Transform
I was trying to compress an image using fourier transform method. The program is successfully running but the compressed image is showing blank(only black).
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FourierTransform does not transform a function on a non-uniform grid? [closed]
I have trouble generating the FourierTransform of a function:
...
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Finding the Fourier coefficints with NFourierCoefficient or FourierCoefficient?
I would like to calculate the Fourier coefficients of the function and then plot them on the fourier transform of it, as well as on the Fourier series of it.
This is what I do:
...
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How to generate a step-wise function over a Fourier interval $[-\pi,\pi]$ for a piecewise function?
I have the following piecewise function:
y[t_] == Piecewise[{{2, -2 < x < -1}, {1, -1 < x < 0}, {2,
0 < x < 1}, {3, 1 < x < 2}}];
...
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1
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Derive Parseval's theorem in one dimension
Parseval's theorem (in one dimension) is a fundamental result in the theory of Fourier transforms. If $f(t) \Leftrightarrow F(\omega )$ are Fourier transform pairs and $t$ (time) and $\omega$ (...
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Is it possible to compute the Fourier transform with Integrate in all cases where FourierTransform succeeds?
I am trying to write a function that generalizes the Laplace and Fourier transforms, but I'm having trouble getting Integrate to play along. The function is called <...
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Tiff image height fft
I wanted to import .tiff image to Mathematica and then plot fft of z values (height) of the image i. e. values which are translated to color in the image.
I know that total time to create picture was ...
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`TerminatedEvaluation[RecursionLimit]` while computing the Fourier series of a signal
I need to compute the Fourier series of the signal below (the vertical blue lines of its first period are strangely omitted by calling Plot[f[t], {t, 0, 20}]!).
<...
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Periodogram and frequency
On the x axis of periodogram, one should have either a period or frequency. What frequency is used in Periodogram --- angular or ...
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Fourier series solution for Laplace equation in polar coordinates results in Power::infy and Infinity::indet
Definition of function f
f[θ_] = 1 + Cos[2 θ] + Sin[3 θ]
Plot[f[θ], {θ, 0, 2 π}]
Computation of the Fourier coefficients
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`Periodogram` returning only 1/0 error
I have a large dataset and would like to get a Periodogram (I saved the data as CloudObject):
...
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1
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Evaluating Fourier transform in mathematica [closed]
I am trying to evaluate the expression
FourierTransform[[m (a^2 - t^2 - I g t)]^-1, t, ω]
in Mathematica. It gives me the error message that "Syntax: "[m(...
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Handling singularities like (x-y) in the denominator while evaluating double integrals
I have to solve an Integral of the following type
...
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Error in Discrete Fourier Transform
Consider this data. I would like to plot it via it Fourier discrete sine transform. However, I am getting a slight offset, as seen here
...
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Mathematica doesn't seem to be able to compute the Fourier transform of the Haar orthonormal basis over $L^2(\mathbb{R})$
Consider
F[x_, n_, m_] := 2^{n/2}*WaveletPsi[HaarWavelet[], 2^{n}*x - m]
A paper I am reading uses a different convention of the Fourier transform than Mathematica'...
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How to expand the wave-length of a time-series in Mathematica?
I have a set of coordinates that represent a time series for a wave train, ampitude/seconds.
An example of the time series is here:
As shown in previous posts, I extract the coordinates on a segment ...
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How to perturb data along a midline?
Consider the following data, which can be obtained here
ListLinePlot[data, Frame -> True]
I want to perturb the previous data around a defined midline, which ...
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Animating a wave function
I have a wave equation which is generated from the command FourierSeries.
The generation of the time-component $FD[t]$ is given by:
...
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Conversion of wave-reading using Fourier transform gives strange output
In relation to this post, I tried a new method in converting wave-readings into coordinates, and then generate the Fourier series from the coordinates.
The method encompasses three steps:
Harvest ...
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An unknown defect with an approach in constructing scaled coordinates for obtaining and plotting Fourier series
I am having trouble scaling a set of coordinates and generating these coordinates into stepwise functions.
I start with the points from a plot:
...
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Is there a built-in equivalent to numpy's fftfreq?
I recently learned that python's numpy package contains a function called fftfreq (documented at numpy.fft.fftfreq) which is ...
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Decomposing an eigenfunction of helmholtz equation into plane waves
I have defined a region and found the eigenmodes of the 2D Helmholtz equation in it:
...
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Cannot generate a Fourier series of a function [closed]
I am trying to generate the fourier series of a function. The function is constructed from a series of points:
...
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