Questions on the discrete and continuous Fourier analysis functions of Mathematica, as well as the FourierSeries` package.

learn more… | top users | synonyms

9
votes
0answers
311 views

Proving (self) similarity with Mathematica - Reccurrence Plots, Similarity Plots etc

I posted this question in math.se but given the sheer tumultuous 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 ...
6
votes
0answers
128 views

Possible bug with FourierTransform linearity

Each component is easily transformed but the sum is not: FourierTransform[f''[x], x, k] FourierTransform[f'[x], x, k] ...
6
votes
0answers
132 views

Fourier transform over a custom dimension

I have a multidimensional array A. Fourier[A] finds the discrete Fourier transform over all dimensions. How to find discrete ...
4
votes
0answers
108 views

The same analytical expression gets inconsistent FourierTransform results

I have an expression which is just a linear combination of plane waves, and I'd like to calculate FT of it. I know what I will get should be a bunch of delta functions, but it turns out Mathematica ...
3
votes
0answers
95 views

How to do Fast Fourier transform (FFT) for singular functions?

I want to do a 3-dimensional FFT on this function $\frac{\cos (x) \cos (y) \cos (z)-\sin (x) \sin (y) \sin (z)}{\left((1.0001+\sin (y)+\cos (z))^2+(0.0001+\cos (x)+\sin (z))^2+(0.0001+\sin (x)+\cos ...
3
votes
0answers
37 views

What are good/best practices to take the Fourier transform of an InterpolatingFunction?

I have a function which I have obtained from numerical integration of a differential equation, and I would like to take its Fourier transform. What are good practices for doing this? To make things ...
3
votes
0answers
114 views

Fourier transformation of HeavisideTheta functions

I want to find 2D-Fourier transformation of the function given below f = HeavisideTheta[y1]*HeavisideTheta[y2 - y1] For the purpose, I use built-in function in ...
2
votes
0answers
59 views

Workarounds for a possible bug in the linearity of FourierTransform

This is somewhat similar to this question, except the problem I am encountering is to do with Fourier transforms of scalar multiples of functions and their derivatives. I wish to input ...
2
votes
0answers
80 views

calling CUDA library functions

Mathematica has some predefined CUDA functions, like CUDAMap, CUDAFourier, etc. My question is how can one call functions which are part of CUDA library but not part of predefined Mathematica ...
2
votes
0answers
57 views

Why does setting $Assumptions make my Fourier transforms slow?

Consider these Fourier transforms ...
1
vote
0answers
53 views

Fourier transform an expression to obtain a distribution?

I have this expression for the correlation function for a rigid rotating molecule: $G(\tau) = 4 \pi \int \omega ^2 P_2[\cos (\omega \tau)] P(\omega) \, \mathrm{d}\omega \quad [1]$ where $P_2$ is a ...
1
vote
0answers
72 views

Is it the right output for Fourier?

I am learning Fourier Series at university so I wanted to do something with Mathematica to calculate frequency spectrum and harmonics of whatever function I create. This is what I have until now after ...
1
vote
0answers
413 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
0answers
32 views

Issues with zero frequency component in discrete Fourier transform

I'm having trouble with the Fourier function at the moment. I'm solving a set of differential equations with NDSolve, then need to extract the spectrum associated with the curve below: So i use ...
0
votes
0answers
31 views

Discrete Fourier Normalization

I have a problem using the Fourier command applied to the square of an exponential function. I would like to compare the theoretical result (called ...
0
votes
0answers
64 views

Calculating the recursion at the Fourier domain

I would like to calculate the following recursion with mathematica $$f_n(x)=\int_{B}^{A}f_{n-1}(x-\omega)f(\omega)\mbox{d}\omega\quad\quad f_1(w):=f(w)$$ This is simply the convolution of $f$ with ...
0
votes
0answers
57 views

Discrete Fourier Transform and data manipulate

I solve a system od ODE and i save the discrete solution (i.e.: x,y,vx,vy, or a subset of it) in a file. Then i try to call the DFT on this file but the problem is that i must have also the time in ...
0
votes
0answers
69 views

Recognizing a generalized function as zero

Consider the following expression: HeavisideTheta[x]HeavisideTheta[-x] Mathematica will not simplify it further. But $\Theta(x)\Theta(-x)$ is zero if considered ...
0
votes
0answers
98 views

Cross-correlation in SDEs

Is it possible to derive a cross-correlation function between a stochastic variable and a state-variable in an SDE, such as for the simple model here, or better between two state variables in a two ...