Questions tagged [fourier-analysis]
Questions on the discrete and continuous Fourier analysis functions of Mathematica, as well as the FourierSeries` package.
438
questions
2
votes
0answers
40 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
87 views
Slow execution in Fourier analysis [on hold]
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
1answer
65 views
Interpretation of 'InverseFourier' function when results are complex
I am using 'Fourier' to perform a discrete fourier transform/DFT on a time-limited/finite time signal, x[n]. From my understanding, I can interpret each element of the output list (call it output1) of ...
0
votes
0answers
40 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
29 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
94 views
+50
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
37 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
46 views
2
votes
1answer
59 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
55 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
35 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
27 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
205 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
68 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
138 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
83 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
25 views
Using `Integrate` and or `FourierTransform`
I have some general questions about Integrate and FourierTransform. Firstly with ...
1
vote
0answers
61 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
88 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:
...
0
votes
1answer
46 views
Integration not working
Can't seem to get this integration to work. s, n, b, b, l are all constants.
...
0
votes
0answers
43 views
Trouble with computing a Fourier transform
I am able to compute the Fourier transform of the general form Exp[-Sqrt[t]] as shown here:
...
0
votes
0answers
41 views
Discrete convolution power
In my previous question we have discussed the posibility of various definition of convolution of power function within Mathematica. Now the question is "How to define convolution power in Mathematica ?...
1
vote
0answers
46 views
Why does FourierSinSeries return zero? [closed]
I wonder why FourierSinSeries returns 0 in this case:
...
7
votes
2answers
188 views
Strange result of FourierCosCoefficient on $\cos^2 t$
The following strange answers were just reported in Mathematics.SE. The OP was asking about the Fourier cosine series of the function
$$\cos^2t=\frac12(1+\cos 2t).$$
That question is about WA, but ...
0
votes
0answers
38 views
Fourier on chosen dimensions
I have a data set DATA in 4 dimensions $A \times B \times C \times D$
and I want to use the Fourier function net only on the 2 ...
0
votes
0answers
30 views
Evaluating Fourier coefficients when Exponential terms are present
I am trying an analytical solution for a 3D Laplace equaition, and just wanted to know if I could use the symbolic calculation capabilities of Mathematica to calculate the Fourier coefficients
...
0
votes
2answers
157 views
Fourier series of an arbitrary periodic piecewise function
Let's take a switch function as an example:
$
u(t)=
\begin{cases}
1, & \text{$0<t<dT_s$} \\
0, & \text{$dT_s<t<T_s$}
\end{cases}
$
How can I get Fourier series of it in ...
9
votes
1answer
174 views
Which FFT algorithm does `Fourier[…]` use?
Does anyone know which Fast Fourier Transform algorithm Mathematica uses to compute a Discrete Fourier Transform using Fourier[...], and is there any option to ...
4
votes
1answer
117 views
Why does Fourier give me a different picture than ImagePeriodogram?
I want to take a 2D fourier transform of some data, but when I try this I get unexpected results. When I use ImagePeriodogram I get something that looks like I ...
3
votes
2answers
188 views
Fourier Transform to help guess with NonLinearModelFit
I imported some data in Mathematica which I cleaned a bit. This process went well. I also managed to plot it, and tried to take the Fourier transform of the data and plot it again. I'm not sure if I ...
1
vote
0answers
54 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 ...
0
votes
1answer
60 views
DFT and continuous Fourier transform gives different result? [closed]
I am working on the inverse Fourier transform of $\frac{\sqrt{|k|}}{i(|k|-\omega)-\Gamma}$ with $\omega=100, \Gamma=1$. For continuous Fourier transform, I get the following result:
...
1
vote
1answer
70 views
applying a fourier sin series fit and then doing a fourier transform
I tried to fit a fourier sin series onto this data with the two different following codes.
...
1
vote
2answers
91 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 ...
0
votes
1answer
79 views
Plot beat waves spectrum
I have a signal composed of 3 waves oscillating at a high frequency (~10^15 Hz) separated in frequency by 10MHz. I want to simulate the resulting beat wave spectrum. I am expecting a two-peak spectrum,...
1
vote
2answers
68 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 (-...
1
vote
3answers
174 views
Another way to calculate frequency from Fourier transform
I have some trouble with calculating frequency after Fourier transform.
My code:
...
1
vote
1answer
57 views
Mathematica stuck at running symbolic multidimensional Fourier Transform
I'm trying to compute the analytical FT of a bidimensional exponential decay as follows:
$f_E(\vec{x}) = \exp \left( - \sqrt{ (\vec{x} - \vec{\mu})^T \Sigma^{-1} (\vec{x} - \vec{\mu}) } \right)$
...
0
votes
1answer
39 views
FourierTransform and Integrate don't agree [closed]
With the input
f[t_] := Cos[2 Pi t]
FourierTransform[f[t], t, w, FourierParameters -> {0, -2*Pi}]
I get ...
0
votes
0answers
28 views
Problem with symmetry and anti-symmetry of the fourier coefficients
let's say that I have a set of data
...
0
votes
0answers
50 views
Is there a way to find the Region of Convergence along with the Laplace Transform?
This is what I've tried so far.
Is the inequality of the conditional expression the Region of Convergence?
Why doesn't LaplaceTransform Generate conditions here?
...
1
vote
1answer
99 views
How to get exact frequencies in the time response using InverseFourier?
I have amplitude data varying with frequency for a signal. From that I want to generate time response in such a way so that if I take Fourier I can get the ...
3
votes
0answers
174 views
Deconvolution using Fourier transforms
I have a 2D signal in the form of a function $g(x_m,y_m)$ given as
$$ \begin{aligned}
g(x_m,y_m) = \ & \int^{\infty}_{-\infty} \mathrm{d}x_o \ \mathrm{d}y_o \ \frac{1}{\varepsilon^2} P(x_o - x_m,...
1
vote
0answers
78 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 ...
2
votes
1answer
203 views
Generate noise time series with given data's PSD
I have PSD data as a 1D array, function of frequency(rad/sec). It is like powerspectrum for damped oscillator.
Considering 3 modes, PSD is shown here.
I want to generate noise time series which ...
0
votes
1answer
114 views
2
votes
2answers
146 views
Fourier Phase Angle Interpretation
I am trying to fit the following tide data (taken from here) with a sinusoidal curve that looks like the following: displacement+amplitude * sin(t w - ph), where t is the independent variable, w is ...
-1
votes
1answer
29 views
Result from FourierCosCoefficents does not appear to be linear [closed]
f3 and f4 below produce the same output (more or less) but
the coefficient in f3 does not appear to be the sum of f2 and f1 (which it should, uiam).'
...
0
votes
0answers
57 views
Need to find Fourier series of the following graph
Need to find Fourier series of the following graph.....question is also written in figure.
2
votes
1answer
102 views
Unexpected behaviour of PowerSpectralDensity
I recently wanted to calculate the power spectral density of a surface profile. I was happy to find out that there is a built in PowerSpectralDensity[] function in Mathematica (version 10). However, I'...
