Questions on the discrete and continuous Fourier analysis functions of Mathematica, as well as the FourierSeries` package.
17
votes
3answers
1k views
Can one find the beat of a tune with Fourier analysis?
I'm trying to find out if it's possible to find the beat of a tune by Fourier analysis with Mathematica. I'm taking a 44.1 kHz sample sound and hoping that I might get a nice peak for a frequency ...
12
votes
4answers
1k views
Numerical Fourier transform of a complicated function
Say I have a function $f(x)$ that is given explicitly in its functional form, and I want to find its Fourier transform[1]. If $f$ is too complicated to have an analytic expression for $\hat f(k)$, how ...
12
votes
4answers
353 views
+50
Digital filter of image in Fourier space
Consider the contour plot below, of a function f(x,y) - which is calculated numerically by solving some equations.
If one looks carefully, one can observe two types of waves, to the left and right of ...
12
votes
2answers
816 views
How to make Fourier behave like FourierTransform?
I'm not very experienced with Fourier Transforms, so there may be something inherently wrong with attempting to do this, but how can I make the discrete Fourier behave like the continuous ...
12
votes
2answers
238 views
Parallelization of distinct array write access from subkernels
I'm working on an implementation of a multivariate FFT, which is (or at least should be) highly parallelizable due to the row-column-algorithm. However, i can't figure out how to implement that. The ...
11
votes
1answer
1k views
Coulomb potential as a Fourier transform
It is well known from theory that the Coulomb potential can be obtained as a Fourier transform in the following way:
$$ \int \frac{\mathrm{d}^3p}{\left( 2 \pi \right)^3} \frac{e^{\mathrm{i} ...
8
votes
3answers
2k views
Plotting Partial Sums of Fourier Series
I'd like to plot some partial sums for a Fourier Series problem, but I am not sure if the output I am getting is correct. I want to be able to plot the partial sums and the function on the same graph. ...
8
votes
1answer
290 views
How can I obtain a zero-filled Fourier transform, as produced by MATLAB's fft?
The MATLAB FFT function, fft(X,n), can be used to return the n-point DFT. This effectively extends the original signal, X, to ...
8
votes
1answer
296 views
FourierSeries for rational function looks wrong
I have the following code:
ser[x_] = FourierSeries[(\[Pi]^2 + a)/(3 x^2 + a), x, 10] // N // Chop
It gives me some series, which I then try to plot. And ...
7
votes
2answers
159 views
Speed up Fourier for Booleans
I'm calculating a bit of the power spectrum of a two color cellular automaton using:
...
7
votes
2answers
288 views
How to approximate a given WAV file with trigonometric series?
I'd like (together with a few people) to prepare a presentation about Fourier series for middle/high school students. I thought it might be quite cool to play a violin sound from, say, a WAV file, ...
7
votes
0answers
150 views
Proving (self) similarity with Mathematica - Reccurrence Plots, Similarity Plots etc
I posted this question in math.se but given the sheer tumultous number of questions that keep appearing on math.se and also given that I am trying to accomplish this in Mathematica, I thought I'd post ...
6
votes
1answer
284 views
Speeding up numerical Fourier Transform
I wrote this function NFourierTransform, which takes a function $f(k)$ and numerically calculates the fourier transform integral for discrete values of $k \in ...
5
votes
2answers
1k views
Fourier Transform of a Step Function
I'm trying to obtain the form of a sinc function that I know I'm suppose to get in Mathematica. I'm doing this because I intend to do a lot with Fourier Transforms and I'd like to know I'm not missing ...
4
votes
0answers
82 views
Computation of Hankel Transform using FFT (Fourier)
To address circular symmetric cases of 2D Fourier Transformations the so called Hankel Transform can be applied (for a detailed derivation of the relation between the 2D Fourier transform and the 1D ...
2
votes
2answers
2k views
Does Mathematica implement the fast Fourier transform?
Is there a fast Fourier transform in Mathematica? Although looking in the help I could not find one.
I am looking to implement the equivalent of fft in MATLAB.
2
votes
1answer
82 views
Tough Inverse Fourier Integral: why does the sign matter?
I'm computing the Inverse Fourier Integral of
((a^2 + omega ^2) c^2)
/((b^2 + omega^2) ((r^2 + omega^2 - omegaInt^2)^2 + (2 omegaInt r)^2))
...
2
votes
1answer
710 views
Plotting the frequency spectrum of a data series using Fourier
testData = Table[N@Sin[500 x], {x, 0, 100}];
ListLinePlot[Abs[Fourier[testData]], PlotRange -> Full]
Gives me
Which I do not expect because the Fourier ...
2
votes
0answers
280 views
Fourier Coefficients in Mathematica [duplicate]
I'm calculating Fourier Coefficients by hand and trying to verify them in Mathematica.
However, in Mathematica I get them wrong by a factor of 2. Is there some part of the Mathematica functions I'm ...
1
vote
2answers
529 views
Computing the minimum number of terms required in a Fourier series to achieve a particular upper bound on the error
In a Fourier series, the maximum error bound is the difference of the function and the partial sum of its Fourier series. Within an interval, as we increase the number of terms of partial sums, the ...
1
vote
2answers
328 views
Obtaining the Fourier transform of an operator
We know that if we have a function $f(x)$, and we call $g(\omega)$ its Fourier transform, then the Fourier transform of $x f(x)$ is
$$\imath \frac{\mathrm{d} g(\omega))}{\mathrm{d}\omega} $$
and ...
1
vote
1answer
150 views
How can I find the Fourier series from discrete data?
I would like to define the function with Fourier series when I just have discrette data. (I don't have a specific function).
I can draw the graph using the data, but I don't have a idea how can I get ...
1
vote
1answer
110 views
Fourier transform of sampled data
I have got some impulse response data that I would like to transform via Fourier to get the amplitude-frequency characteristics of the performing loudspeaker. The ...
1
vote
0answers
237 views
Doing local FFT on huge 3D vector data cell mesh and visualizing it spatially?
Simulation type:
I'm running a simulation with the OOMMF micromagnetics package
http://math.nist.gov/oommf/
where are magnet is represented by a mesh of 3 million cells, it gets excited by a ...
0
votes
2answers
347 views
How to calculate FDCT
I'm new to Mathemtica and I'm trying to calculate Discrete Cosine Transformation FDCT. I found the FourierDCT built-in function, but not DCT, so I need to implement it. I have tried couple of ideas ...
0
votes
1answer
207 views
Fourier series spectrum argument and absolute value [closed]
Started playing with Mathematica a week ago. Now I'm on some more "advanced" stuff and really can't figure out what is happening.
I'm trying to get the spectrum of this signal, $x(t) = 110 ...
0
votes
2answers
212 views
Discrete FFT of non-periodic signal excited by short pulse
Say I have a signal F(t) which represents a excitation by a pulse (so it is not periodic and declining to zero amplitude). According to this answer, for instance, ...
0
votes
1answer
90 views
How to manipulate a Fourier sine series?
I would like to plot the Fourier sine series for $f(x) = x$.
I would like to manipulate the parameter n from $0$ to $10$ and plot the sine waves over $(0,1)$. My ...
0
votes
1answer
438 views
discrete Fourier transform
As an answer to my code I will get a periodic discrete time dependent function called "data" which I want to get a Discrete Fourier transform of it using just one period of it,but I think some thing ...
0
votes
1answer
174 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:
...
0
votes
0answers
53 views
Algorithm for the Ornstein-Zernike equation with Percus-Yevick (PY) approximation [closed]
I want to solve the Ornstein-Zernike equation using the Percus-Yevick approximation in Mathematica and acquire the numerical solution for the $g(r)$ function. I found a python algorithm here which is ...
0
votes
0answers
74 views
Fourier transform of a signal
I have problem of finding right answer for my problem.
Here is my equation:
$$E(t)=\sum_{n=1}^{\infty} c_n \sin\left(\frac{n \pi}{T}t\right)$$
What have I done:
I have a notebook asking for 3 ...
0
votes
1answer
88 views
Error messages when using NInverseFourierTransform
I have two functions that I need to inverse Fourier transform and I was trying to get Mathematica to help me. I tried simply using theInverseFourierTransform ...
0
votes
0answers
130 views
Obtaining fourier transform for Root Raised Cosine pulse
I have been trying to obtain the Fourier transform for time domain root-raised-cosine pulse using Mathematica. The answer I'm getting from Mathematica is not the correct answer. When I input the ...
0
votes
0answers
79 views
How to get Contours/maxima for an image in a useful form [closed]
I have some images in which I would like to find the locations of various maxima, plus the contour lines at a level e.g., 50% of that maximum intensity.
As a first step, I did a FourierDCT on the ...
0
votes
0answers
246 views
Mathematica's definition of Fourier Transform [closed]
I would to know how is defined this function in Mathematica:
FourierTransform[expr,t,ω]
That function give the Fourier Transform of a complex function of real ...
