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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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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 ...
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]] ...
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 ...
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 (-...
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 ...
278 views

### How to find the Fourier Transform of a list?

I have a list (list) in the form of {x,y} as ...
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 ...
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 ...
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: ...
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 ...
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 ...
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 ...
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: ...
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 ...
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 <...
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 ...
45 views

Observe: ...
131 views

### Strange behavior of FourierSinCoefficient`

FourierSinCoefficient works normally like this and the result is checked with Integrate. ...
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 ...
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 ...
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: ...
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. ...
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." ...
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 ...
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, ...
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 ...
52 views

### Why does FourierSinSeries return zero? [closed]

I wonder why FourierSinSeries returns 0 in this case: ...
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 ...
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 ...
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 $(-\frac{1}{2},\frac{1}{2})$:- ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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, ...
216 views

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 ...
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 ...
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) ...