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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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3 votes
1 answer
378 views

### Fourier series using DFT

I am trying a simple example to do a discrete Fourier transform. My goal is to use DFT to find the frequencies that have built the time signal and then to a good approximation, use DFT data to find ...
2 votes
1 answer
170 views

• 1,885
0 votes
2 answers
114 views

### Computing a highly oscillating Fourier Transform

I'm trying to compute the Fourier Transform of a diverging and oscillating function:: ...
• 139
3 votes
2 answers
320 views

### 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). ...
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3 votes
1 answer
214 views

1 vote
0 answers
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### 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 ...
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 ...
3 votes
1 answer
223 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 ...
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4 votes
1 answer
129 views

### FourierTransform of a simple two-dimensional function

FourierTransform correctly computes the transform of a one-dimensional "box" function, or HeavisidePi[x]: ...
• 41.9k
3 votes
3 answers
881 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 ...
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6 votes
3 answers
540 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 ...
6 votes
2 answers
710 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 ...
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3 votes
1 answer
90 views

### Nice output for FourierTransform

I want to demonstrate FourierTransform in a lecture. However if you give FourierTransform a differential equation it does not ...
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0 votes
1 answer
69 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 ...
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 ...
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0 votes
1 answer
123 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 ...
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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. ...
2 votes
3 answers
184 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 ...
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1 vote
0 answers
109 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 ...
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1 vote
0 answers
97 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 ...
0 votes
0 answers
137 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 ...
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1 vote
0 answers
99 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 ...
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3 votes
1 answer
102 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 ...
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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 ...
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 ...
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-1 votes
1 answer
84 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 ...
1 vote
1 answer
128 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: ...
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0 votes
1 answer
103 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 ...
1 vote
1 answer
76 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: ...
8 votes
2 answers
341 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 ...
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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.
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1 vote
1 answer
192 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: \nabla\cdot(\overset{\scriptscriptstyle\leftrightarrow}{\sigma} \nabla \Phi) = 0, \label{Eqn:OhmsLaw}\...
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5 votes
1 answer
101 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 ...
1 vote
1 answer
93 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 ...
1 vote
1 answer
159 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 ...
3 votes
0 answers
341 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 ...
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2 votes
1 answer
62 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:. ...