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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How to manipulate a Fourier sine series?

I would like to plot the Fourier sine series for $f(x) = x$. I would like to manipulate the parameter n from $0$ to $10$ and plot the sine waves over $(0,1)$. My ...
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3answers
156 views

Problem with Fourier Transform output

I am trying to evaluate this FT, but Mathematica takes long time without output ...
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1answer
53 views

How to Mathematica applied discrete Fourier transform to matrix?

I am new user of Mathematica, sorry if my question odd. I not understanding, how to Mathematica apply the discrete Fourier transform for matrix: ...
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3answers
165 views

Is there a way to speed up this Fourier transform and optimise the results?

Can anyone suggest a method of speeding up the evaluation of the following Fourier transform? FourierTransform[UnitStep[t] Exp[-t/τ] Cos[(m t + ω0 ) t], t, ω] I'...
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1answer
118 views

Unexpected behaviour of PowerSpectralDensity

I recently wanted to calculate the power spectral density of a surface profile. I was happy to find out that there is a built in PowerSpectralDensity[] function in Mathematica (version 10). However, I'...
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1answer
634 views

Problem with Fourier transform

How to define a top hat function with plot also at opening and closing value? and How to plot a Fourier transform of the function?
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2answers
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PDE in Fourier space

I have a coupled PDE. How can I convert the equation from $(x,t)$ to $(p,t)$, the Fourier space in MATHEMATICA? \begin{equation} \frac{\partial c}{\partial t} +\frac{\partial d}{\partial t} = -4\...
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1answer
857 views

Cut off frequency of low pass filter

I have a data here, I want to make sense of Lowpass filtering function in Mathematica.I do not fully understand units of cut off frequency in this option since the data is in frequency space. What I ...
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1answer
220 views

Fourier transform question

Consider the fourier transform FourierTransform[1/((Cosh[x] + 1) (Cosh[x]^2 - 1)^(1/2)), x, w] If I execute the above line, Mathematica thinks for several ...
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1answer
102 views

Change FourierParameters in CUDAFourier

CUDAFourier does not have option FourierParameters. I need to change its convention. It has default ...
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1answer
562 views

Fourier Transform of Square Functions [closed]

I wanted to visualise at how the frequency spectrum of square waves changes with duty. But I got stuck at the first hurdle: FourierTransform[SquareWave[x], x, w] ...
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2answers
475 views

FourierSeries command , for arbitrary period T?

ExptoTrig[FourierSeries[Piecewise[{{-Pi,-2Pi<x<=0},{Pi,0<x<=2Pi}}],x,3]] You can see, the function goes from $(-2\pi,2\pi]$ But Wolfram Alpha gives a ...
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1answer
352 views

How to remove the frequency noises in a Fourier Transformation on an experimental data?

This question is a follow-up to a previous question. I need to perform a Fourier Transformation on an experimental data in time-domain, as shown in Fig 1. With the kind help from Daniel Lichtblau ...
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1answer
163 views

Need help for Discrete Fourier Transform on an experimental data

I have an experimental data, which is basically a time-domain triangle function. Part I: In theory The time-domain figure is shown in Fig. 1(a), and the corresponding frequency-domain figure is ...
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1answer
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Discrete Fourier Transform of a vector defined on a 3D lattice

In my research I need to compute the Discrete Fourier transform of a vector defined on a 3D lattice (a cube) to the "reciprocal" lattice. This is quite new to me so before proceeding i wanted to be ...
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1answer
2k views

Integrate message: can't prove Integration limits are real

I'm working on solving differential equations through Fourier series, I made a function to help me calculate the coefficients that looks like this: ...
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1answer
2k views

Fourier transform of sampled data

I have got some impulse response data that I would like to transform via Fourier to get the amplitude-frequency characteristics of the performing loudspeaker. The ...
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1answer
446 views

How to perform this numerical Fourier transform?

For $t\in\mathbb{R}_{\ge 0}$ and $s\in\mathbb{R}$, let $$f(t)=\begin{cases}\int_{0}^{t}\exp\left(-\frac{1}{1-s^{2}}\right)\,ds,&|s|<1, \\ 0,&|s|\ge 1\end{cases}$$ I plotted this without ...
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1answer
53 views

What is the correct way to represent this sum?

The summation of Fourier series of Sin[x-x[i]] at three location x[1] to x[3] is: ...
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1answer
68 views

NIntegrate option for FourierSeries

I would like to use FourierSeries but it is very slow. My guess is that it is because it uses symbolic integration: ...
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1answer
206 views

Finding periodicity of multidimensional data?

I have a data set consisting of measurements of an $n$-dimensional vector $\mathbf{x}(t)$, at $N$ distinct time points $t_i$. The time points $t_i$ are equally spaced. I need to find the dominant ...
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1answer
115 views

How to calculate a numerical multidimensional Fourier series

The Fourier series tutorial here describes a number of different commands for numerically finding Fourier series and their coefficients. However, they only seem to work for one dimensional Fourier ...
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1answer
72 views

Sum of Fourier Sine Series Not Giving Original Function

When I plug the below sum (from here) into Mathematica 12.1.1, why do I get something different from the original function ($1 + x^2$)? ...
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2answers
121 views

Issues with Fourier transform in M.12.1.0

I am using M. Version: 12.1.0. In version 10, I got the result right away.So, Why mathematica (12.1.0) is not able to solve this problem? ...
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1answer
656 views

Generate noise time series with given data's PSD

I have PSD data as a 1D array, function of frequency(rad/sec). It is like powerspectrum for damped oscillator. Considering 3 modes, PSD is shown here. I want to generate noise time series which ...
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1answer
237 views

Re and Im relationships without Abs among Fourier, FourierTransform, InverseFourier, and InverseFourierTransform

Is there a way to make Fourier's Re and Im components separately track the results of ...
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1answer
492 views

How to find the Fourier Transform of a list?

I have a list (list) in the form of {x,y} as ...
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1answer
765 views

Fourier Transform plot of a piecewise function

I'm working with financial data. I used "Find Formula" to find an approximate function and then I applied FourierTransform to it. Here are the function and the Fourier Transform: ...
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1answer
410 views

Fourier transform along only one dimension of 2D array

I'm a relative newbie to Mathematica Before you flag me as duplicate, note that I have read and studied "Fourier transform over a custom dimension" as best I can. I cannot understand the answer, it ...
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1answer
221 views

Implement inverse discrete-time Fourier transform

In Mathematica after version 9. We had ListFourierSequenceTransform to do discrete-time Fourier Transform, but we do not have the inverse function. If we peform it ...
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1answer
761 views

Partial derivative with Dirac Delta as initial condition

I am trying to reproduce the Faynman-Kac results from this Wikipedia page: Faynman-Kac This is the equation that I am trying to solve: $$ \frac{\partial w(t,x)}{\partial t} = \frac{1}{2} \frac{\...
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1answer
79 views

FourierTransform a function doesn't give result when variable is 0

I am trying to get a Fourier Transform of a function. However it doesn' work when the variable is 0. I used Mathematica 8.0 on a Windows Server 2008 R2 system. The code is as follows: Defining ...
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1answer
888 views

Plotting a periodic function [duplicate]

My question is the following: how can I plot a function repeatedly? By following some topics here I found some basic information about using Fourier series. This is what I made: ...
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1answer
55 views

Speed up the “FourierCoefficient” of SPWM wave

I want to view the Fourier coeffs of one SPWM (1) wave: ...
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1answer
124 views

Why I get negative values on using periodogram after Fourier analysis?

sorry for bothering you with this question today. I am trying to analyze wave data that was produced using a wave tank. The period used for the waves is 1.7s, the waves encountered an obstacle at some ...
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1answer
177 views

Implementing an anti-alliasing filter in Mathematica

I'm experimenting with FFT simulations. I'm generating transient data at the some sampling rate, down-sampling this (mimicking a device's behavior) to 2048 points. Then take the FFT using ...
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1answer
148 views

How to get exact frequencies in the time response using InverseFourier?

I have amplitude data varying with frequency for a signal. From that I want to generate time response in such a way so that if I take Fourier I can get the ...
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1answer
161 views

Discrete Fourier transformation from ASCII (for noob)

I am not familiar with Mathematica (I am a physicist programming in Fortran) and my knowledge of it is very limited, unfortunately. I would like to perform the Fourier trasform of a lightcurve which ...
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1answer
189 views

Fourier Transform of a symbolic expression

Hello I would like to do the Fourier Transform of H1'[t - L2[t]/c - L2primo[t]/c] I know that its transform has to be: ...
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1answer
105 views

Using ''Module' and 'Table' to Plot 'Fourier'

I'm trying to make a function that outputs a plot given a particular parameter, whilst using the Mathematica functions Module, Fourier, and Table. This is what I've come up with thus far. ...
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1answer
170 views

Reconstruct signal using InverseFourier [closed]

I start from a signal, I do discrete Fourier transform of the signal, and I want to get back this same signal doing a discrete inverse Fourier transform. However, when I do so, I do not obtain the ...
2
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1answer
164 views

Two different results for same symbolic integral

I am trying to compute the following integral $\int_0^\infty dk \frac{e^{i k a}}{k^2}[\sin(kb)-kb\cos(kb)]$ When computing it as-is, i.e, with the code ...
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1answer
1k views

Fourier transformation of solution of differential equation

I'm trying to plot a Fourier transform of solution of differential equation. I have tried with: ...
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0answers
47 views

Triple infinite summation of a 3D Fourier series

I'm trying to evaluate the equation below excluding the case when $n_x=n_y=n_z=0$. I know this equation converges everywhere except where x,y, and are all multiples of $2\pi$. I've attempted breaking ...
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0answers
91 views

Use List convolve for aligning images

I am trying to align images of point spread functions using a convolution. Before doing it on real data, I wanted to try on simulated data. I have no problem with the 1-D case where I create 2 ...
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0answers
91 views

Fourier Cos coefficient vs Integrate vs common sense

I was trying to find out what the (discrete) Fourier transformation of the following function is $$ f(\nu, u) = \frac{\sinh \nu}{\cosh \nu - \cos u} $$ So at first, I tried to evaluate a fancy MMA ...
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0answers
68 views

2d vs 1d FourierTransform

According to the documentation, the multidimensional Fourier transform is defined as $$ \frac{1}{(2\pi)^{n/2}} \int_{-\infty}^\infty \int_{-\infty}^\infty \cdots f(t_1, t_2, \dots, t_n) \mathrm e^{\...
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0answers
161 views

Fourier transform of imaginary exponential with absolute value argument [closed]

When asked to compute FourierTransform[Exp[(-I*Abs[x])], x, k, FourierParameters -> {1, 1}] Mathematica returns ...
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0answers
194 views

Analysis of the periodic data by the maximum entropy method

I am trying to get the frequency spectrum of periodic data. Since the data set is short, the outcome of the frequency peaks are not sharp enough for me to do further analysis. I know the spectrum can ...
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0answers
76 views

Determining Periodicity with Fourier?

Note: This question has previously been marked as a duplicate of What do the X and Y axis stand for in the Fourier transform domain?. While the answer will likely have an overlap, so the question ...

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