Questions tagged [fourier-analysis]
Questions on the discrete and continuous Fourier analysis functions of Mathematica, as well as the FourierSeries` package.
466
questions
1
vote
1answer
42 views
Partial sums and Fourier series approach
I am trying to plot the partial sums for $N=5,10,15,20$ of the Fourier series of $f(x)=(1-x^2)^2$ and $-1<x<1.$ I have:
...
0
votes
1answer
54 views
Complex Fourier method for a function
I am trying to calculate the complex fourier series of $f(x)=\cosh x$ for $-\pi<x<\pi$ . I tried
...
1
vote
1answer
54 views
Fourier series for a function
I am trying to calculate the fourier series of $f(x)=\sin x$ for $0<x<\pi$ and $f(x)=0$ for $-\pi<x<0$ and make the plots. I tried
...
4
votes
0answers
73 views
Problem with FourierTransform
Let us consider
a = FourierTransform[Log[RealAbs[x]]*Sin[x], x, s]
$\frac{i \sqrt{\frac{\pi }{2}}}{2 \left| s+1\right| }-\frac{i \sqrt{\frac{\pi }{2}}}{2 \...
0
votes
1answer
68 views
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?
...
1
vote
1answer
65 views
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 ...
1
vote
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.
...
0
votes
1answer
32 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. ...
0
votes
1answer
71 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 ...
1
vote
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 ...
0
votes
1answer
47 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?
...
0
votes
1answer
44 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 $a=\exp(i b)$, ...
1
vote
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]]
...
1
vote
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."
...
0
votes
0answers
40 views
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 ...
2
votes
1answer
45 views
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:
...
3
votes
1answer
47 views
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 ...
0
votes
2answers
57 views
Finding Fourier formula to fit a given data set
I am trying to find a model with a Fourier basis for this data:
...
0
votes
1answer
68 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 ...
2
votes
2answers
123 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?
...
0
votes
1answer
86 views
Identifying the three frequencies using fourier transform
The following simple function has clearly three frequency components:
...
2
votes
1answer
91 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 ...
0
votes
0answers
21 views
3
votes
1answer
117 views
How to set up a Fourier transform?
I am having trouble figuring out how to set up the Fourier transform to:
...
3
votes
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} & ...
2
votes
1answer
56 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
votes
1answer
69 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
votes
0answers
48 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)
...
0
votes
1answer
36 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 ...
1
vote
1answer
60 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
vote
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 ...
2
votes
3answers
149 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'...
2
votes
0answers
46 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
votes
1answer
97 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
votes
0answers
54 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.
...
0
votes
0answers
40 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).
...
2
votes
1answer
162 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 ...
0
votes
0answers
62 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}[...
0
votes
1answer
50 views
2
votes
1answer
69 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
votes
1answer
76 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 ...
0
votes
0answers
50 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 ...
1
vote
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, ...
1
vote
4answers
226 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 (\...
0
votes
1answer
83 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
votes
1answer
158 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 ...
1
vote
1answer
116 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 ...
0
votes
0answers
29 views
Using `Integrate` and or `FourierTransform`
I have some general questions about Integrate and FourierTransform. Firstly with ...
1
vote
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 ...
0
votes
1answer
112 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:
...
