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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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757 views

Trouble with Fourier transform of Exp[-Sqrt[x]]

First time trying to do something "real" in Mathematica, I am having trouble getting it to calculate this Fourier transform. It runs for a long time, then just prints the input expression. ...
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2answers
188 views

frequency shift in Fourier transform

Have a bit of an analysis issue with Fourier transform of a sinusoidal signal: I have a piece of signal that represents spatial scanning of a pattern. xcoordinate is distance and y is amplitude. I'm ...
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1answer
118 views

Why am I having trouble calculating this ODE?

I'm trying to compute solutions for $$\frac{\partial^{4}}{\partial t^{4}}\mathcal{F}_{x}u(\xi,t)-|\xi|^{4}\mathcal{F}_{x}u(\xi,t)=0$$ ...
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1answer
227 views

Writing a Fourier Series Equation

I am trying to program a Fourier Series equation that I will use for a normed fit that is not a least squares fit. If I write ...
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2answers
190 views

Partial Sums of Fourier Series [closed]

It does not want to plot anything? Please, help me understand why. Thank you ...
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1answer
267 views

Fourier transformation of multidimensional list [closed]

x is a list containing 7 trajectories (Dimensions[x] = {2726, 7}) of which I want to calculate the FFT. ...
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2answers
1k views

Get Y-Axis of FFT in decibels

I am trying to make a plot of a sound file similar to Audacity's FFT plot which looks like this when the x-axis is on a log scale: My plot of the same sound file (below) has the problem that the ...
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1answer
164 views

How to use fast Fourier transforms (FFT) to calculate derivatives of a function?

Suppose we have a function numerically defined at pseudospectral collocation points ...
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1answer
101 views

Implementation of discrete Fourier Transform in Matrix Form

I am trying to gain an in depth understanding of how discrete fourier transforms work, and consequently I am trying to implement the discrete fourier transform myself in the form of a matrix. First ...
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2answers
506 views

Re and Im of fourier transform for shifted rectangular pulse

I'm currently trying to vizualize the relation between time and frequency domain and their behavior for a single rectangular pulse regarding different paramters. A special focus is set on the real Re ...
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1answer
1k views

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
54 views

Fourier Analysis of a .aiff file

I'm trying to use Mathematica to perform Fourier Analyses on sound files, but I'm not sure how to get the Frequency Spectrum from the .aif file. The instructions I have say: use Mathematica’s Play ...
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1answer
561 views

Fourier Parameters

I need to use the built-in function Fourier, to get the Fourier transformation of a list of numbers. Unfortunately, I would need to set the second argument of the FourierParameter option to a non-...
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1answer
54 views

Passing arguments correctly to FourierTransform

I'm trying to define the functional $T$ on test functions $f$ and $g$ in Mathematica 11, where $$T(f,g) = \int_{-\infty}^\infty\hat{f}(x)\hat{g}(-x)\,dx$$ So I have written: ...
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1answer
92 views

Weird plot for the discrete Fourier transform of a normal distribution compared to Matlab

In mathematica, why does Print[ListPlot[Fourier[RandomReal[NormalDistribution[], {100000}]],PlotRange -> All]]; return an empty plot, sometimes with a random ...
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1answer
918 views

Detecting beat frequency using FFT

I wrote Mathematica FFT code that works for non-beat signals, eg. Sin[2*Pi/20*x] and more complicated but I can't obtain beat frequency of Sin[2*Pi*(10)*x] + Sin[2*Pi*(11)*x]. Also, what is general ...
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2answers
179 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? \begin{equation} \frac{\partial c}{\partial t} +\frac{\partial d}{\partial t} = -4\...
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1answer
59 views
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2answers
254 views

Plotting fourrier series generated from sum of sine functions [duplicate]

I'm using Mathematica 11.0.1.0 (Student) on macbook. I'm trying to plot a basic square wave function. The sum function return the results of sine function series, I could not see anything from ...
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1answer
234 views

Changing Dirac Delta to Kronecker Delta? [closed]

I have a program where I actually need Kronecker Delta instead of Dirac Delta Function. Is there a way to make such a switch in Mathematica 11. Example: ...
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1answer
175 views

FourierTransform breaks function symmetry

The fourier transform of a seemingly simple function gives me a complicated result: (I imaginary unit) ...
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1answer
187 views

Fourier discrete transform [duplicate]

Code is given below ...
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1answer
583 views

Image Filtering in the frequency domain

Here is a good starting to fiter image in the frequency domain lena = ColorSeparate[ImageResize[ExampleData[{"TestImage", "Lena"}],{121,121}]][[1]]; (Create a ...
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1answer
203 views

How are Fourier transformations calculated? [duplicate]

Lets say my function is $$f(t)=\left\{\begin{matrix} 1 &, -T_p/2\leq t \leq T_p/2\\ 0& , |t|>T_p/2 \end{matrix}\right.$$ than a Fourier transformation is calculated $$F(j\omega)=\int_{-\...
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1answer
125 views

NFourierTransform do not show all points, even change PlotPoints and Exclusions

Needs["FourierSeries`"] I try solve the numerical Fourier transform of this function: ...
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1answer
983 views

Fourier Series and epicycles - How to find the radii and angular velocities from a function's Fourier Series expansion [duplicate]

The following code is a bit clumsy, but it constructs a variable number (n) of epicycles using the values from the radii and angularVel tables that follows the path of a parametric given as a sum of ...
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1answer
274 views

Discrete Fourier Transformation

Assuming I have a function $f(x)$. I can use a numerical Fourier transformation: NFourierTransform[] to find some points of $F(\omega)$. How can I do the same ...
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2answers
558 views

How do I extract peak frequencies? [closed]

Suppose I have large text file filled with numerical data. Then I do Fourier operation with this file and plot the result: ...
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1answer
485 views

DFT: why are frequencies mirrored around the frequency axis?

I want to apply Mathematica's DFT procedure, Fourier[], to a Gaussian. Why a Gaussian? Because I know the analytical result. So I define ...
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2answers
2k views

How to calculate the phase spectrum

I have the following frequency characteristics in the Fourier domain: $$H(\omega)=\frac{-\omega^2}{63170s^{-2}-\omega^2+355.1s^{-1}i\omega}$$ How do I find the phase spectrum from this? I should ...
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1answer
589 views

Extracting out the Fourier modes of a series, and using these to reconstruct data series

I would like to extract the most important frequency modes from a data set which exhibits strong annual periodicity, as well as some (less) important shorter-term frequency components. The following ...
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1answer
106 views

Convolution in Fourier domain

I am computing the convolution of a disk Img in 2D numerical matrix form with a kernel Ker in the Fourier domain but the output ...
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1answer
97 views

applying a fourier sin series fit and then doing a fourier transform

I tried to fit a fourier sin series onto this data with the two different following codes. ...
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1answer
67 views

Mathematica stuck at running symbolic multidimensional Fourier Transform

I'm trying to compute the analytical FT of a bidimensional exponential decay as follows: $f_E(\vec{x}) = \exp \left( - \sqrt{ (\vec{x} - \vec{\mu})^T \Sigma^{-1} (\vec{x} - \vec{\mu}) } \right)$ ...
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3answers
486 views

Find Fourier Series/Coefficients with Mathematica

Hello I want to find the Fourier series and/or the coefficients for a function like the following: or or For the first one I did the following: ...
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1answer
306 views

2D Fourier transform of annulus

I have an annulus and I'd like to the take the 2D Fourier transform of it, my code: ...
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2answers
156 views

NFourierTransform gives wrong result

This is my code: ...
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1answer
309 views

How to calculate the complex Fourier coefficients and its partial sum?

Using complex exponentials (without FourierTrigSeries): \begin{align*} f(x) &= \sum\limits_{ - \infty}^{ + \infty} {{c_n}{e^{2 \cdot \pi \cdot i \cdot n \cdot ...
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2answers
148 views

How to obtain real number after Fourier?

I have a table of list of complex numbers. I constructed the table in the following way: the table contains odd number $N$ of elements. The $N/2+1$ element of table is real. $N/2+2$ element is complex ...
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1answer
431 views

finding fourier coefficient of a parametric curve [closed]

There is a function in mathematica FourierCoefficient for finding fourier coefficients of a periodic function, but it requires the mathematical expression as input. ...
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1answer
271 views

get period from non-uniform discrete data by Fourier transfomation

I found that it seems the fourier function only treat the discrate data with equal timeinterval, as an experiment, let us consider the following example: ...
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2answers
326 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
433 views

How to solve time dependent coupled differential equations using Floquet method?

I have coupled differential equations D[X[t], t] == M[t] X[t] + R[t] where ...
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1answer
704 views

Inverse Fourier transform

I am dealing with an inverse Fourier transform of a sampled complex function, $H(\omega)$. I want to obtain a real transformed function $h(t)$, which means that $H(-\omega)=H^{\ast}(\omega)$ has to be ...
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1answer
226 views

Why does Fourier give a large error in MachinePrecision?

Consider this code: ...
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1answer
890 views

Problem with Fourier and InverseFourier function

I have the following code Image[img, ImageSize -> 300] data = ImageData[img]; fdct = Fourier[data] tdata = InverseFourier[fdct]; Image[tdata] but it seems to ...
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1answer
44 views

Fourier transform gives wrong result

The expression I InverseFourierTransform[FourierTransform[1/t, t, w]/w, w, x]//FullSimplify gives EulerGamma + Log[Abs[x]] ...
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2answers
99 views

Polynomial fit and Fourier transform plot

I'm pretty new to Mathematica so excuse me for obvious questions. I have a dataset, second column contains invoice amount and the first column contains days passed between each invoice date starting ...
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2answers
81 views

How do I find the n-th Fourier coefficient of a function?

I have to define the function f: π for x ∈ (-1,1) 0 for all the others. How do I find the n-th coefficient of this function in the Fourier series expansion for (-...
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1answer
185 views

Get frequency axis in Fourier transform (and save them)

I am trying to get the Fourier transform of a light-curve (with an even number of points, 300, and equally spaced in time, 6.9 seconds) and my problem is to get the frequency on the x-axis. I can ...