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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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FourierTrigSeries doesn't know Jacobi–Anger expansion?

Mathematica returns FourierTrigSeries[Cos[Sin[t]]^2, t, 2] unevaluated. This can easily be done by hand with the Jacobi–Anger expansion (or Jacobi–Anger identity). ...
ions me's user avatar
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3 votes
1 answer
211 views

FourierTransform result different than expected

FourierTransform[Exp[-a t]*UnitStep[t], t, w] gives the following result $$\frac{1}{\sqrt{2 \pi } (a-i w)},$$ but the answer should be $$\frac{1}{\sqrt{2 \pi } (a+i ...
Jeffrey Pattavina's user avatar
4 votes
0 answers
87 views

Different results produced by FourierTransform and InverseFourierTransform

I try to calculate the inverse Fourier transform of (k2^2 - k1^2)/(k1^2 + k2^2) using FourierTransform and ...
leeppp's user avatar
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3 votes
0 answers
68 views

Inconsistent solutions in two representations

Consider the following differential equations: ...
phy_std's user avatar
  • 143
1 vote
1 answer
84 views

How can I use fast Fourier transform to divide into low and high frequency components? [closed]

I have this data (where x is time (seconds) and y is diopters (D)): ...
Zarabu's user avatar
  • 81
1 vote
1 answer
90 views

What's the difference between FourierSinCoefficient and FourierSinSeries in in terms of results?

Let's assume having defined a sawtooth: saw[t_] := 2*(SawtoothWave[t + 0.5] - 0.5) Now, we'd like to compute sine fourier coefficients for that sawtooth. We may do ...
djjb1974's user avatar
0 votes
0 answers
45 views

Memory-Efficient FFT of Sparse Array

I have to take the Fourier transform of quite a large 2D array (2^15 by 2^15, but I'll use 2^10 as an example here). My array is mostly zeros, and since Fourier can ...
az123p's user avatar
  • 239
0 votes
1 answer
113 views

Numerical Fourier transform

I am having issues trying to numerically Fourier transform the following function \begin{equation} f(x) =\frac{1}{x^6}\sqrt{4m^2x^2+x^4}\log\biggm(\frac{2m^2 + x^2 + \sqrt{4m^2x^2+x^4}}{2m^2}\biggm) \...
MathZilla's user avatar
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4 votes
1 answer
201 views

Fourier Transform of 2D data using Fourier

I don't understand the documentation of Fourier. My goal is the get the coefficients of the Fourier-series (i.e. $\sum_{n\in \mathbb{Z}} c_{n,m} e^{inx+imy}$) of ...
Confuse-ray30's user avatar
5 votes
1 answer
276 views

FourierTransform and InverseFourierTransform are not inverses when using non-default FourierParameters

FourierTransform and InverseFourierTransform are inverses of each other when using the default ...
tparker's user avatar
  • 1,856
2 votes
1 answer
144 views

FourierCosCoefficient for function with singularity

FourierCosCoefficient is way more powerful than I expected. For example, ...
Leo's user avatar
  • 131
3 votes
1 answer
54 views

Inconsistency between FourierTrigSeries and FourierCosCoefficient

I have the following function defined for a quasi-square wave: ...
MNairA's user avatar
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2 votes
2 answers
140 views

Circular function with arbitrary radius and center

I'm looking for an implementation in Mathematica of the generalized circular function $\text{circ}(x, y; R, c)$ of radius $R$ and centre $c=(c_1,c_2)$ such that $$\text{circ}(x, y; R, c)=\begin{cases}...
Noobgrammer's user avatar
1 vote
0 answers
168 views

How to Model a Parametric Fast Fourier Transform in Mathematica?

I'm using this code which evaluates the FFT of my original signal (which is a time series). Using the Manipulate function of Mathematica it is possible to vary the ...
Giuseppe Vonella's user avatar
0 votes
0 answers
37 views

Why FourierSequenceTransform cannot be applied to a List (discrete samples) of data?

Wikipedia says the following: In mathematics, the discrete-time Fourier transform (DTFT) is a form of Fourier analysis that is applicable to a sequence of discrete values. … The DTFT itself is a ...
shamil khal's user avatar
3 votes
1 answer
219 views

Tooltip over Fourier transform of an image

This link is to a question showing how to display a Fourier transform of an image. I'd like to build upon the linked solution to make an interactive demonstration, surely using ...
David G. Stork's user avatar
4 votes
1 answer
128 views

FourierTransform of a simple two-dimensional function

FourierTransform correctly computes the transform of a one-dimensional "box" function, or HeavisidePi[x]: ...
David G. Stork's user avatar
3 votes
3 answers
879 views

Mathematica doesn't give the correct value of an integral

I want to calculate the following integral with Mathamtica Integrate[ E^(−2 x I) (Log[Abs[Cos[x − a]]] + Pi I/2 Sign[Cos[x − a]]), {x, 0, 2 Pi}] where $a$ is a real ...
gaoqiang's user avatar
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6 votes
3 answers
527 views

Sum of sinusoids at the same frequency but with different amplitudes and phases

Three sinusoids at the same frequency are superimposed: Cos[3.1 - t] + 5 Cos[π/4 + t] + 2 Sin[0.3 + t] How can the resulting oscillation be stated in the following ...
saturnscalypso's user avatar
6 votes
2 answers
683 views

Convert MATLAB code solving 1D wave equation via FFT using ode45 into Mathematica code

I don't quite understand the process of solving differential equations by MATLAB. It seems that it doesn't need the explicit function to specify the required solution, but only needs to input the ...
mozeq's user avatar
  • 295
3 votes
1 answer
87 views

Nice output for FourierTransform

I want to demonstrate FourierTransform in a lecture. However if you give FourierTransform a differential equation it does not ...
Hugh's user avatar
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0 votes
1 answer
65 views

Pointwise convergence of Fourier series: partial sum animation not rendering plot

I'm new to Mathematica (13.3) and I'm attempting to demonstrate the pointwise convergence of the Fourier series for the square wave function f in particular, by showing via Animate/Manipulate that as ...
Pascal Tchakouté's user avatar
0 votes
0 answers
35 views

Getting frequency domain data from time domain using Fourier transformation [duplicate]

I have a dataset following cosine function [e.g. cos(200t)] in time domain. In frequency domain two sharp lines should appear at -200 and +200. I have to do Fourier transform (or Fast Fourier ...
P Pyne's user avatar
  • 453
0 votes
1 answer
115 views

Trying to plot the Fourier transform solution to the heat equation on Mathematica [closed]

I have gotten the solution of the heat equation as where f(y) is the initial heat distribution which I have been given as f(x) = e^([Sigma]x^2). I am supposed to plot this at the value of sigma 1, 2 ...
yen's user avatar
  • 1
0 votes
0 answers
71 views

How do you create a program to calculate the spectrum of a pulse of arbitrary shape?

Develop a program designed to compute the spectrum of a pulse with an arbitrary shape. My current program might not suitable for solving this problem. ...
Iра Сотник's user avatar
2 votes
3 answers
177 views

How to generate a good Fourier spectrum with incomplete data?

This problem is perhaps a little bit more mathematical than programmatic. I'm using Fourier to analyze my data. Suppose I have a data set ...
Harry's user avatar
  • 2,745
1 vote
0 answers
102 views

Morphing curves with ImagePeriodogram

Any idea how to achieve smooth transition from one image to another (so that the curves are morphing from one shape to another)? I am aware that ImagePeriodogram ...
azerbajdzan's user avatar
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1 vote
0 answers
88 views

How can I construct the inverse of a periodogram?

In this post, instructions are given to construct a periodogram essentially from scratch. How would one write the inverse function? I want to generate a periodogram, do some manipulations, and then ...
user94773's user avatar
0 votes
0 answers
135 views

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 ...
user12588's user avatar
  • 585
1 vote
0 answers
93 views

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 ...
Aerterliusi's user avatar
3 votes
1 answer
98 views

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 ...
138 Aspen's user avatar
  • 1,373
0 votes
1 answer
37 views

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 ...
Cairo Martins's user avatar
1 vote
1 answer
68 views

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 ...
100xln2's user avatar
  • 437
-1 votes
1 answer
76 views

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 ...
Cairo Martins's user avatar
1 vote
1 answer
114 views

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: ...
senseiwa's user avatar
  • 515
0 votes
1 answer
101 views

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 ...
pseudo-goldstone's user avatar
1 vote
1 answer
73 views

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: ...
Runyu Liao's user avatar
0 votes
0 answers
66 views

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 ...
James Linton's user avatar
8 votes
2 answers
334 views

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 ...
David G. Stork's user avatar
0 votes
1 answer
65 views

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.
Lohrasb's user avatar
  • 359
1 vote
1 answer
172 views

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}\...
Charlie's user avatar
  • 506
5 votes
1 answer
100 views

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 ...
Athanasios Paraskevopoulos's user avatar
1 vote
1 answer
87 views

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 ...
Athanasios Paraskevopoulos's user avatar
1 vote
1 answer
156 views

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 ...
shamil khal's user avatar
0 votes
0 answers
70 views

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 (...
sgdsgyhetwaraw's user avatar
3 votes
0 answers
322 views

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 ...
Baoxiang Pan's user avatar
2 votes
1 answer
60 views

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:. ...
Teodoro Marinucci's user avatar
0 votes
1 answer
113 views

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 ...
Andrew's user avatar
  • 10.6k
1 vote
3 answers
176 views

Obtaining better Fourier series for a piecewise constant function

I have the give wave-train: and I extract the given set of points: ...
Superunknown's user avatar
0 votes
0 answers
64 views

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 ...
Lohrasb's user avatar
  • 359

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