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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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1answer
107 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 ...
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1answer
52 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
105 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
94 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
218 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 ...
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1answer
278 views

How to find the Fourier Transform of a list?

I have a list (list) in the form of {x,y} as ...
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1answer
198 views

normalization of convolution product when using Fourier transform

I'm trying to calculate the convolution of two probability density functions (PDFs) defined on the real axis: a normal distribution (with \[Sigma] > 0 and ...
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3answers
116 views

TrigReduce applied to certain terms? Finding coefficients of trig terms

I have an expression that involves trig functions of t and y. I would like to find the coefficients of ...
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1answer
570 views

Automatically finding frequency

For example we have a sinusoidal function and we want to find frequency of this function/ For those we use Discrete Fourier Transform. Code: ...
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1answer
94 views

Integrating doesn't work in some cases

I tried to calculate below integral but there was no response. Integrate[Exp[-t Abs[k]^a - I k x]/Abs[k]^a, {k, -Infinity, Infinity}] Could anyone find a way ...
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1answer
307 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 ...
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1answer
317 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 ...
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1answer
808 views

Plotting a periodic function [duplicate]

My question is the following: how can I plot a function repeatedly? By following some topics here I found some basic information about using Fourier series. This is what I made: ...
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1answer
209 views

Deriving the Fourier Coefficients Formulas with a Manual Procedure

I already know that there are built-in functions to compute the Fourier coefficients but I want to derive their formulas manually. In fact, I want to obtain the final well-known formulas for the ...
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2answers
326 views

Parseval identity in one side Fourier Transform

Is there any posibility to apply Parseval identity(energy in time domain is equal to freq. domain) on One/Single-side Fourier transform? In other word for "standard" FT the test Mathematica can be <...
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2answers
201 views

DataRange in plotting Fourier

I'm trying to estimate a frequency spectrum of a given discrete function. I have a file which is filled of values of Sine-function $sin(t)$, where $t$ runs from $0.0$ to $100.0$ and a discrete step is ...
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1answer
45 views

Puzzling result for CharacterisicFunction and InverseFourierSequenceTransform

Observe: ...
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1answer
131 views

Strange behavior of `FourierSinCoefficient`

FourierSinCoefficient works normally like this and the result is checked with Integrate. ...
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1answer
125 views

Two dimensional NIntegration failure - non-numerical values

I've got this function: E0[x0_, y0_, z_]:= A/w[z]*Exp[-(x0^2 + y0^2)/(w[z]*w[z])]*Exp[(I*2*Pi*(x0^2 + y0^2))/(λ*2*R[z])]*Exp[I*ϕ[z]]; Where the ...
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1answer
965 views

Plotting partial sums of Fourier sine series

How do I plot this on Mathematica version 5.2? $\frac{4}{\pi} \sin{x} + \frac{4}{3 \pi} \sin{3 x} + \cdots + \frac{4}{(2 N+1) \pi} \sin{(2 N+1) x}$ over $x \in [-\pi,\pi]$ for $N= 3, 6, 12, 24$. I ...
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1answer
1k views

Fourier transformation of solution of differential equation

I'm trying to plot a Fourier transform of solution of differential equation. I have tried with: ...
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1answer
79 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. ...
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0answers
53 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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0answers
38 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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0answers
33 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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0answers
66 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 ...
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0answers
52 views

Why does FourierSinSeries return zero? [closed]

I wonder why FourierSinSeries returns 0 in this case: ...
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0answers
59 views

Fourier parametric plot running into “Iteration limit of 4096 exceeded.”

I am trying to create a fourier drawing tool like this but am running into an iteration limit on larger images. Being quite new to mathematica, how could I go about fixing this / making the program ...
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0answers
122 views

Fourier transform of non-uniform sampled data

I need to perform an inverse Fourier transform of this set of data, which is in the frequency domain (the x-axis is in $\mu$Hz). However, I'm having two doubts $-$ firstly, this spectral spacing is ...
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0answers
41 views

How to force the output to be in terms of a specific function?

I have a rectangular function rect[t], which is a window function with values of $ 1 $ in the interval $ (-\frac{1}{2},\frac{1}{2}) $:- ...
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0answers
206 views

2D Fourier transform of a diffraction pattern Mathematica vs FourierPainter

We are trying to make sense of the numbers provided by the PC program FourierPainter for a 2D Fourier Transform of a diffraction pattern. We would like to evaluate the ratio of the zeroth harmonic ...
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0answers
157 views

Fourier | Examples | Applications | Frequency Identification: high resolution: what trick is this?

My question is regarding one of the examples in the Documentation Center for the built-in symbol Fourier: Fourier | Examples | Applications | Frequency Identification Fourier is used to find the ...
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0answers
107 views

wavelet fourier transform

I want to do wavelet Fourier transform of my data but I have few doubts in this. 1)first of all what is octive and voice command here when i am changing value according to that my plot is changing but ...
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0answers
216 views

Comparison of Discrete Cosine Transform and Discrete Wavelet Transform

I would like to compare the sorted coefficients of the Discrete Cosine Transform with that of the Discrete Wavelet Transform using the Haar wavelets. From theory, the discrete wavelet transform offers ...
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0answers
192 views

Inverse Fourier Transform of Poisson Characteristic Function?

The follow line is returning without evaluation: InverseFourierTransform[ CharacteristicFunction[PoissonDistribution[1], t], t, w] It is meant to output ...
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0answers
134 views

Fourier Transform(first use)

This is in continuation of the question I asked Wrong evaluation of integral in Mathematica? But I will try to make it self contained. I have a periodic function ...
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0answers
82 views

Wrong behavior of Inverse Fourier Transform of DiracDelta[x]/x

The following fails to compute: InverseFourierTransform[DiracDelta[w]/w, w, x] But if we add a, ...
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0answers
216 views

Multidimensional numerical Fourier transform

I'm trying to numerically compute the Fourier transform of the following bump function: $$\hat{r}(k)=\int r(x)e^{ikx}dx$$, where $r\in C^{\infty}_{0}(\mathbb{R}^{2})$, namely: $$r(x)=\begin{cases}\...
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1answer
139 views

FourierCosSeries of DiracDelta[x] mismatch

When I do* FourierCosSeries[DiracDelta[x - 0.0001], x, 5] I get as a result ...
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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: ...
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0answers
83 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: ...
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0answers
142 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 ...
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0answers
141 views

Is oscillation seen in data signal or noise? [closed]

I have some experimental data which is well-fitted by 40 terms of a Fourier series. I want to know if the oscillation exhibited is signal or noise. I evaluated the code shown below to plot my data in ...
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0answers
494 views

Normalization of discrete Fourier transform not obvious [duplicate]

I'm trying to write some code (eventually in Fortran) to quickly calculate the Voigt profile using the convolution theorem. However, I ran into some trouble using the Intel MKL FFT library, so I'm ...
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0answers
263 views

Assumptions don't work as expected in FourierTransform

The 2D rectangular function and its Fourier Transform is $$ g_{in}(x,\,y) = rect(\frac{x}{x0}) \, rect(\frac{y}{y0}) \quad \xrightarrow{\mathscr{F}} \quad G_{in}(u,v) = x0 \, y0 \, sinc(\pi u x0) \, ...
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0answers
212 views

Perform a Fourier Transform on a wavelength scan

I have a plot of the power transmitted through a device as a function of wavelength, from 1500 to 1600nm. There is some Fabry-Perot noise, plus I suspect some other regularities. I would like to ...
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0answers
122 views

Discrepancy between laplace and fourier transform of gaussian

The function in question is Exp[x^2/2] for x>0 Laplace transform should be the same as the fourier transform since the function is absolutely integrable. Fourier: They are indeed the same ...
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0answers
186 views

Discrete Fourier Transform baseline subtraction

I am trying to remove sinusoidal variability from a set of evenly-spaced intensity vs. time data. These data contain periodic events that are separated by a normalized (but sinusoidally variable) ...
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0answers
89 views

Monitor Progress of a function (Fourier[] in my case)

I am using PSD = Abs[Fourier[normedAutoValues, FourierParameters -> {-1, 1}]]; normedAutoValues contains around 200 *10^7 ...
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0answers
162 views

PeriodogramArray or PowerSpectralDensity?

could anyone explain what is the difference between PowerSpectralDensity[data,omega] and PeriodogramArray[data]? When I plot them (starting from the same set of data of course) I get two different ...