# 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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### Impulse response function h(t) of Gauss functions as a stimulus and response

From the basics of the signal theory the impulse response function (IRF) can be calculate like (L=Laplace transformation): L[x(t)]= X(s) , L[y(t)]= Y(s) and transfer function H(s)= Y(s)/X(s), then IRF ...
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### Speed up the “FourierCoefficient” of SPWM wave

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

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### how to compile the function correctly?

My calculations are running terribly slow (for a larger number of variables than in the given code). I can't compile the function correctly. Can anyone help me? ...
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### Fourier Spectral Analysis [closed]

I'm currently working on an engineering exercise that goes as such: I know that I need a step function to model the square waves, but I'm having trouble finding the right functions to generate the ...
114 views

### Finding frequency of oscillation of an particle by Fourier analysis of the trajectory [duplicate]

I am trying to find the resonant frequency of a particle by Fourier analysis of the trajectory. Here is the data file. ...
37 views

### Fourier sine series

p[t_] := (1/12) Sign[Sin[428 \[Pi] t]] + (11/12) Sign[ Sin[428*2 \[Pi] t]] FourierSinSeries[p[t], t, 10]] I want to expand this function but it takes forever. ...
74 views

### Function values ​at many points

I would like to receive the results of the function for 3 points. I would like x and y to replace the coordinates of three points to get 6 results - due to 2 values ​​of the coefficient "k". x and y ...
129 views

### Finding the phase difference between fundamental harmonics of two waveforms [closed]

I have two periodic non-sinusoidal waveforms $WV1$ and $WV2$ (See Figure). I want to extract the fundamental components of these two (i.e. $WV1_{F0}$ and $WV2_{F0}$) and find the peak amplitudes and ...
58 views

### Double Fourier series - value at a point [closed]

I would like to receive the value of the series at point x->1,y->1. Where is the mistake? ...
51 views

### Fourier transform of 1/(ax(t)-1) where x(t) is the euler formula

Let $x(t)=\exp(i k t)$ where $k$ is a constant I know the Fourier transform of $x(t)$ is a Dirac function How can I express the Fourier transform of: $$\frac{1}{ax(t)-1}$$ where $a=\exp(i b)$, ...
102 views

### Fourier transform gives wrong result

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

### InverseFourierSequenceTransform gives zero

I am wondering why Mathematica(12) in the following code InverseFourierSequenceTransform[1,kx,x] gives different results if we just change "1" to "1." ...
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### Finding Fourier transform of a quantity v/s theta (0 to 360 degrees)

I have a physical quantity (experimentally measured) lets say T whose variation I have measured with angle (theta in degrees). I want to find out the Fourier components of this quantity with respect ...
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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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### How does the Fourier transform take its input?

I'm using the Fourier command and I'm wondering how does it take its imput. I know that it takes a list of numbers representing a function of time and it gives back a list of numbers representing a ...
80 views

### Finding Fourier formula to fit a given data set

I am trying to find a model with a Fourier basis for this data: ...
328 views

### Discrete fourier transform and convolution — scaling factor?

I am trying to convolve a square wave (a diffraction grating phgrating with slits size \[CapitalLambda]) with a point spread ...
216 views

### Figuring out the frequency components using FFT [duplicate]

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

### Identifying the three frequencies using fourier transform

The following simple function has clearly three frequency components: ...
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### 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 ...
335 views

### How to set up a Fourier transform?

I am having trouble figuring out how to set up the Fourier transform to: ...
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} & ...
215 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 ...
78 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: ...
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### 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 ...
100 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 ...
44 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 ...
189 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'...
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 ...
137 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....
199 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. ...
85 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). ...
194 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 ...
120 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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### Exact Fourier coefficient from large expression

I have a relatively simple analytic expression ...
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### 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! ...
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### 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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### 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, ...
246 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 (\...
105 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 ...
245 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 ...
158 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 ...