# 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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1answer
85 views

### An numeric Inconsistency in mathematica

Here are my mathematica command and output: ...
1answer
187 views

### Fourier discrete transform [duplicate]

Code is given below ...
1answer
139 views

### FourierCosSeries of DiracDelta[x] mismatch

When I do* FourierCosSeries[DiracDelta[x - 0.0001], x, 5] I get as a result ...
1answer
337 views

### Fourier Transform accelerogram seismic

I have a seismic accelerogram. I tried to apply the Fourier Transform to interpolate function, but dosn't work. So, i applied the ...
1answer
422 views

### Convert omega to frequency in FourierTransform [closed]

FourierTransform function in mathematica returns Fourier transform of input function in omega. but I need to get Fourier transform of input function in hertz(frequency) that output should be ...
1answer
2k views

### Plot output of FourierTransform in mathematica [closed]

I'm a too newbie in mathematica.I've gotton my output correctly as Shown below: ...
1answer
255 views

### FourierTransform doesn't work properly [closed]

Here is my code FourierTransform[A*B*(Sin[\[Pi] *B* x]/(\[Pi] *B *x)) cos[2* \[Pi]* x *C], x, f, FourierParameters -> {1, -1}] but it doesn't work in ...
1answer
213 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 ...
1answer
757 views

### Finding peaks on a Periodogram

I am currently working on a school project involving modelling sound recordings of piano notes. I have used the periodogram function to graph my recording and would like to find the peaks of this ...
1answer
97 views

### Change FourierParameters in CUDAFourier

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

### Why isn't Mathematica outputting the inverse fourier transform of this function?

I'm brand new to Mathmematica, so please be nice. I don't understand where I'm going wrong. I just need to use the method of inverse fourier transform on this wavefunction to get the momentum-space ...
1answer
562 views

### Fourier in Mathematica different from octave [duplicate]

First I create a table of sin(x) within 0, 10 ...
0answers
41 views

### Fourier transform of an equation [duplicate]

I have the following equation: $$m \frac{d^2 x}{dt^2} = -Kx - \alpha \frac{dx}{dt} + f(t)$$ Which I introduced into Mathematica as: ...
1answer
571 views

### finding Frequency of Sinewave data using Fourier

CONTEXT I read 5 different related posts but I do not understand how to interpret mathematica's output for my situation. ...
0answers
68 views

### Finding covariation between datasets [closed]

For me this is a very fascinating problem, which I however lack the ability to deal with as well as the nomenclature to describe properly. (Please feel free to edit the title). The conditions are the ...
1answer
329 views

### Fourier transform inconsistency

Bug introduced in 5 or earlier and persisting through 11.3.0 On Mathematica 11.0.0 the Fourier transform of $x\theta(x)$ gives the expected result: ...
0answers
89 views

### Laplace transform of rapidly increasing function

Consider the following 3 LaplaceTransform expressions. I believe that the first two are valid (at least for k>0). The third ...
1answer
501 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] ...
1answer
2k views

### Fourier transform of interpolating function [closed]

I want to get a Fourier transform of an interpolating function and plot that Fourier transform: ...
2answers
143 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 ...
0answers
81 views

### evaluate image disorder from FFT?

I have to find some estimates of the disorder in a hexagonal lattice, that is in microscopic images like this (disorderedhex.png): [ I wrote this to simulate these kind of images: ...
1answer
396 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. ...
1answer
266 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: ...
1answer
1k views

### Why Fourier transform is symmetric no matter what interval I choose? [duplicate]

I'm solving a vibration problem. After solving two systems of ODEs (one valid in 0-0.1 and the other in 0.1-1) I get the plot of 3 functions, one of them is this, the plot of the variable $y_w$ (Image ...
1answer
644 views

### NFourierTransform of an interpolating function

I have an interpolating function called rs22 - a solution from NDSolve - which is defined from 0 to about 1 ms. rs22 is a function that reaches a non-zero equilibrium value. (only shown here up to ...
1answer
577 views

### Fourier FFT frequencies [duplicate]

I am using FFT (Fourier) on a dataset that contains the temperature along a rod 1m long. The data is sampled with a spacing of <...
2answers
205 views

### How do I numerically compute the $L^1$ norm of the Fourier transform of a bump function?

I'm trying to compute the following. Let $$f(t) := \exp\left(\frac{1}{t^2 - 1}\right)1_{-1 < t < 1}.$$ This function looks like (it's the standard example of the bump function on Wikipedia). ...
1answer
502 views

1answer
294 views

### How to Plot component frequencies, amplitudes and phases of a mixed signal

I generated a mixed signal by adding two sin waves (whose parameters I can change dynamically) and plotted them. I used the code for findPeriod from here to find the amplitudes, frequencies and phases ...
1answer
97 views

### Reorganise expression as trigonometric polynomial [closed]

I have this expression (obtained with Expand): ...
0answers
153 views

### 4D Fourier transform of $\theta(t^2 - x^2 - y^2 - z^2)$

Possibly this post of mine is bad style in that I am not a Mathematica user, at least not yet; rather I use the competing Maple. My excuse, if at all acceptable to the present community, is that ...
0answers
134 views

### Fourier Transform for Blazed Fork Grating

I built blazed fork grating on Mathematica and the idea of using blazed fork grating instead of normal one is to eliminate the other diffracted order. So the blazed fork grating will let only the 1st ...
5answers
787 views

### Why isn't LowPassFilter working for these parameters?

First I define a function, just a sum of a few sin waves at different angular frequencies: ...
2answers
759 views

### How to graph the contour of a resulting Manipulate curve

How can the green contour be graphed? ...
1answer
738 views

### Why doesn't Mathematica evaluate FourierTransform[Exp[-t], t, w]?

I am having trouble getting Mathematica to evaluate a trivial Fourier transform. I would like to be able to evaluate the Fourier transform of the right-sided exponential decay function as shown ...
1answer
261 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. ...
1answer
64 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 ...
1answer
220 views

### Fourier transform of Exp[x]/x

Could you please explain why Mathematica gives the following expression when taking Fourier transform of $\exp(\lambda z)/\lambda$? $$\frac{-\log(-z)+\log(z)}{\sqrt{2\pi}}$$ Why the answer does not ...
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 ...
2answers
295 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 ...
0answers
93 views

### FourierTransform a differental-equations [duplicate]

I want to use the command FourierTransform to transform a differential equations from time - domain to complex frequency domain but it don't works. My code is ...
0answers
382 views

### Computation of a Fresnel Diffraction pattern with Discrete Hankel Transform

In the next link: Computation of Hankel Transform using FFT (Fourier) Rainer implemented a great solution given in the next reference: Manuel Guizar-Sicairos and Julio C. Gutiérrez-Vega, "Computation ...
1answer
182 views

### Find the function $f(x)$ by using its fourier expansion

It is easy to find the fourier coefficient and fourier expansion of $f(x)$ function. But I want solve the inverse problem by using Mathematica How to find the function $f(x)$, if I know its ...
1answer
101 views

### How to use a Fourier-transform on variable which is multiplied by a constant

I have tried to do this calculation: ℏ := 1.05457168*10^-34 FourierTransform [ψ[x], x, ℏ*p] but the result is: How can I do it right?
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: ...
1answer
272 views

### Inverse of a Fourier matrix [closed]

I am trying to find the inverse of a Fourier matrix but I am getting confusing results. If R is a Fourier matrix, then ...
2answers
134 views

### Why do I encounter 1/0 expression

I am trying to write my periodical function $f(t)$ in Fourier Series $$f(t)=\frac{a_0}{2}+\sum_{j=1}^Na_j\cos(j 2\pi t/\tau)+\sum_{j=1}^Nb_j\sin(j 2\pi t/\tau)$$ and I know that there is a really nice ...