# 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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### Problem with Fourier Transform output

I am trying to evaluate this FT, but Mathematica takes long time without output ...
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### 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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### 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'...
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'...
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?
226 views

### 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? \frac{\partial c}{\partial t} +\frac{\partial d}{\partial t} = -4\...
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### 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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### 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 ...
102 views

### Change FourierParameters in CUDAFourier

CUDAFourier does not have option FourierParameters. I need to change its convention. It has default ...
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] ...
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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### 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 ...
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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### 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 ...
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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### 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 ...
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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### 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: ...
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: ...
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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### 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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### 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 ($1 + x^2$)? ...
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? ...
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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### 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 ...
492 views

### How to find the Fourier Transform of a list?

I have a list (list) in the form of {x,y} as ...
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: ...
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 ...
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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### 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 ...