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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2
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1answer
120 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 ...
2
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2answers
98 views

Figuring out the frequency components using FFT

The function defined below has three frequencies 2, 4 and 10. How to use the Fourier transform (FFT) to show these frequencies? ...
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1answer
60 views

Identifying the three frequencies using fourier transform

The following simple function has clearly three frequency components: ...
2
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1answer
80 views

FourierTransform frequency

In wikipedia's Fourier Transform site there are tables of important FTs, the thing is that Mathematica always considers angular frequency. Is there a way to get what is in the second column labeled ...
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1answer
2k views

How to do continuous Fourier transform?

I want to do a Fourier transform to the below function by Mathematica. How can I do it? Here $c$, $d$, $a$, $L$ are constants. $$ w(r)= \left\{ \begin{array}{ll} -\frac{c}{\epsilon r} & ...
4
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1answer
87 views

How to set up a Fourier transform?

I am having trouble figuring out how to set up the Fourier transform to: ...
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0answers
18 views

Plotting DiracDelta series

I'm dealing with the Fourier Transform of the following signal: ...
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3answers
410 views

Symbolic Discrete Fourier Transform (DFT), using FFT?

Is there an implementation of a symbolic FFT in Mathematica? I've looked around, but I can't find any; Fourier seems to only give numerical results.
0
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1answer
54 views

Integration not working

Can't seem to get this integration to work. s, n, b, b, l are all constants. ...
2
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1answer
43 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 ...
0
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1answer
570 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: ...
0
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1answer
68 views

Dealing with Root objects in the result of a Fourier transform of a complex impedance [duplicate]

I have a complex impedance which I want to back transform into the time domain. My attempt in MM is: ...
0
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0answers
46 views

What is the representation of the Harmonic Number being used by Mma in this result?

The Fourier Transform of the function F[x_] = (m/Sqrt[\[Lambda]])*Tanh[(Sqrt[x^2]*m)/Sqrt[2]] where all variables are real, and $m>0$ is given by (Mma 11.0) ...
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1answer
33 views

Help with correcting a simple example on FourierCoefficient

I am learning FourierCoefficient and trying to plot Cos with it. Let us find it Fourier coefficients with ...
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1answer
49 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 ...
1
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0answers
36 views

InverseFourierTransform takes me forever

I am trying to solve complicated PDEs using FourierTransfrom and InverseFourierTransform on Mathematica 12.0, but the code below does not give me a result. I do not get any error messages but the ...
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3answers
123 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? ...
2
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1answer
148 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 ...
2
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1answer
434 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?
2
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0answers
44 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 ...
2
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1answer
93 views

Slow execution in Fourier analysis [closed]

The following example executes and plots a Fourier transform of a integrable function. Can anyone suggests why the execution is so slow (about 1 min on a laptop Intel(R) Core(TM) i7-4600U CPU @ 2....
0
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0answers
46 views

Fourier Transform and Inverse Fourier Transform of Lists

I am trying to compute the Fourier transform of a list, say an array of the form {{t1, y[t1]},.....{tn, y[tn]}}; apply some filters in the spectral components, and then back transform in time domain. ...
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0answers
32 views

Fourier transform of a 3D list {x,y,value}

I have a list of x and y coordinates and values corresponding to it. (Note: I don't have a function). ...
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0answers
42 views

How to solve integral equation involving Fourier Series

I have a set of equations involving two anti periodic functions $f(t+T)=-f(t)$ and $g(t+T)=-g(t)$ \begin{cases} f(t)&=J^2g(t)^3 \\ \mathcal{F}[g](\omega_n)&=\frac{1}{-i\omega_n-\mathcal{F}[...
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1answer
49 views

Exact Fourier coefficient from large expression

I have a relatively simple analytic expression ...
2
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1answer
61 views

How to shift function (like RotateRight) in the y direction?

I'd like to shift my graph so the periodogram is centered. I was able to rotate the original using Rotate Right, but now I can't shift the graph in the y dimension. Thank you for your help! ...
0
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1answer
64 views

How to fit one function into the form of another?

I have a slightly complicated periodic function of one variable t, say g[t]. I want to do a least squares fit of that function ...
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0answers
37 views

Harmonic amplitude spectrum

I have simulated an electrical machine in mathematica in discrete calculus. One of the results is three phase currents. My plotted answer is like below: Now I'm looking for harmonic amplitude ...
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0answers
30 views

A newbie question about the use of the FourierSeries functions

Although I have had no previous experience with the Mathematica Fourier Series functions ( or package ), I am writing a tutorial on Fourier Analysis and Transformations in a Mathematica Notebook, ...
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4answers
214 views

How to calculate the Fourier transform of Sinc[b (ω1 - ω2)]?

I would like to calculate the Fourier transform of Sinc[ b (ω1 - ω2)], but there are some problems as follows: My target is $\int _{-\infty }^{\infty }\int _{-\infty }^{\infty }\text{Sinc}(b (\...
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1answer
75 views

How to implement a Fourier series?

I've got a Fourier series (amplitude An and phase Phi, see below) 12 terms which I would like to implement in Mathematica. The ...
4
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1answer
141 views

Decomposition of a time series into sinusoids

I've noticed this interesting study on metatrader 4; see the picture below: Where the financial timeseries is "decomposed" (deconvolved?) into a series of periodic sinusoidal functions. In the ...
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1answer
95 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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0answers
26 views

Using `Integrate` and or `FourierTransform`

I have some general questions about Integrate and FourierTransform. Firstly with ...
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0answers
65 views

Fourier transform calculation never stops [closed]

I'm trying to calculate a Fourier transform and plot it, however the calculation is running for several hours now. I suspect that there is a mistake in my script. Or am I just not patient enough? Is ...
9
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1answer
186 views

Which FFT algorithm does `Fourier[…]` use?

Does anyone know which Fast Fourier Transform algorithm Mathematica uses to compute a Discrete Fourier Transform using Fourier[...], and is there any option to ...
0
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1answer
93 views

Finding frequency from Fourier transform [closed]

I tried to find frequency using Fourier Transform, but notice that my code have some mistakes which I can't find. So, my code is below: ...
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0answers
45 views

Trouble with computing a Fourier transform

I am able to compute the Fourier transform of the general form Exp[-Sqrt[t]] as shown here: ...
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0answers
45 views

Discrete convolution power

In my previous question we have discussed the posibility of various definition of convolution of power function within Mathematica. Now the question is "How to define convolution power in Mathematica ?...
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1answer
137 views

InverseFourierTransform very slow

I determined a distribution dist = SmoothKernelDistribution[ListOfValues];. Then I determined the FT of the PDF, which is the ...
10
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1answer
274 views

Package for fast spherical harmonic transform in Mathematica?

Mathematica's implementation of the Fast Fourier Transform is, naturally, much faster than computing the discrete transform yourself using Sum. The analog of the ...
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0answers
48 views

Why does FourierSinSeries return zero? [closed]

I wonder why FourierSinSeries returns 0 in this case: ...
7
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2answers
194 views

Strange result of FourierCosCoefficient on $\cos^2 t$

The following strange answers were just reported in Mathematics.SE. The OP was asking about the Fourier cosine series of the function $$\cos^2t=\frac12(1+\cos 2t).$$ That question is about WA, but ...
4
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1answer
125 views

Why does Fourier give me a different picture than ImagePeriodogram?

I want to take a 2D fourier transform of some data, but when I try this I get unexpected results. When I use ImagePeriodogram I get something that looks like I ...
0
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0answers
38 views

Fourier on chosen dimensions

I have a data set DATA in 4 dimensions $A \times B \times C \times D$ and I want to use the Fourier function net only on the 2 ...
0
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0answers
34 views

Evaluating Fourier coefficients when Exponential terms are present

I am trying an analytical solution for a 3D Laplace equaition, and just wanted to know if I could use the symbolic calculation capabilities of Mathematica to calculate the Fourier coefficients ...
0
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2answers
187 views

Fourier series of an arbitrary periodic piecewise function

Let's take a switch function as an example: $ u(t)= \begin{cases} 1, & \text{$0<t<dT_s$} \\ 0, & \text{$dT_s<t<T_s$} \end{cases} $ How can I get Fourier series of it in ...
1
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1answer
555 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 ...
1
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1answer
63 views

Mathematica stuck at running symbolic multidimensional Fourier Transform

I'm trying to compute the analytical FT of a bidimensional exponential decay as follows: $f_E(\vec{x}) = \exp \left( - \sqrt{ (\vec{x} - \vec{\mu})^T \Sigma^{-1} (\vec{x} - \vec{\mu}) } \right)$ ...
3
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2answers
195 views

Fourier Transform to help guess with NonLinearModelFit

I imported some data in Mathematica which I cleaned a bit. This process went well. I also managed to plot it, and tried to take the Fourier transform of the data and plot it again. I'm not sure if I ...