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

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31 views

Fourier transform of a real white noise on a 3D cubic lattice [migrated]

I'm facing the following problem: I have a cubic domain of side $L=2\pi$; this domain is divided in a cubic grid, each side is divided in $N$ points, where $N$ is an even integer number. the ...
10
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3answers
2k 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, ...
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0answers
76 views

Incorrect output from InverseFourierTransform

Bug introduced in 8.0.4 or earlier and fixed in 9.0.1 or earlier I am trying to compute the inverse Fourier transform of this expression ...
0
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0answers
25 views

Multidimensional Fourier PDE solution and and exact solution are scaled by $(2 \pi)^{2}$

I'm solving a partial differential equation (Stokes equation) in a periodic domain in three dimensions with fourier transforms. I'm using Fourier[] mathematica routines to perform the discrete ...
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1answer
57 views

Extracting out the Fourier modes of a series, and using these to reconstruct data series

I would like to extract the most important frequency modes from a data set which exhibits strong annual periodicity, as well as some (less) important shorter-term frequency components. The following ...
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1answer
53 views

Fourier Transform on a Sound

I don't really know much above Fourier Transform , or how it's used in Mathematica but I want to know how I can find out, out of which Sin-waves a (static) sound is made of. So for example I take "G" ...
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1answer
53 views

Discrete Fourier Transform of a vector defined on a 3D lattice

In my research I need to compute the Discrete Fourier transform of a vector defined on a 3D lattice (a cube) to the "reciprocal" lattice. This is quite new to me so before proceeding i wanted to be ...
2
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0answers
36 views

Precision loss in FourierDCT

I have high precision data that I want to do Fourier transform with, but it looks like the precision is lost dramatically. ...
3
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2answers
118 views

Compare two shifted signals

I have one set of original data (signal A) and a second set of derived data (signal B) which was computed from A by position rotation (circular shift). Here are the data for the signals (A and B): ...
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0answers
56 views

How to filter my signal?

As you can see, my signal is superimposed by an other sinus which has a slightly longer frequency. I would like to filter this out. I think I can do the filtering process, but there is one step that I ...
0
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0answers
66 views

Using 2D Fourier transform of an image to detect typical wavelengths

I am new to Mathematica, and I have read this post to understand how to perform Fourier transform on an image. My mission is to extract information on the typical distance between the black patches in ...
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0answers
72 views

The inverse Fourier transform of a rather complex function

I am using Mathematica 7.0 and trying to find the Fourier transform of a rather complex function g. The function g is defined by ...
4
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0answers
116 views

Periodogram for irregularly spaced data

I am trying to replicate some existing work on the length of the cycles in certain economic data. Specificially, I am using the Schularick and Taylor (2012) data set to replicate the periodogram shown ...
4
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1answer
107 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 ...
1
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0answers
78 views

Inverse Fourier Transform - wolfram alpha vs Mathematica 9.0

I'm facing an interesting problem. I'm trying to do this simple task: InverseFourierTransform[0.031622*Exp[0.4995ω^2], ω, t] Mathematica can't handle it for some ...
0
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0answers
77 views

Fourier Transformation of a List

As we know the FourierTransform goes a function of t ,for example, f[t] to ...
9
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2answers
196 views

InverseFourierTransform of simple function takes forever

i'm quite new to Mathematica. I'm trying to do something along the lines of: ...
2
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1answer
91 views

Finding periodicity of multidimensional data?

I have a data set consisting of measurements of an $n$-dimensional vector $\mathbf{x}(t)$, at $N$ distinct time points $t_i$. The time points $t_i$ are equally spaced. I need to find the dominant ...
2
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1answer
123 views
1
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1answer
132 views

Discrete Fourier Transform with x axis data?

Usually, Fourier Transform in mathematica is supplied by y data only, like the famous Sin[x] transform example. What if my data is a list of ...
0
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0answers
24 views

Inverse Fourier transform to get real function [duplicate]

I have got a sampled complex function, $H(\omega)$ and know that its inverse Fourier transform has to be real function $h(t)$, which means that $H(-\omega)=H^{\ast}(\omega)$ has to be fulfilled. If we ...
1
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1answer
106 views

Inverse Fourier transform

I am dealing with an inverse Fourier transform of a sampled complex function, $H(\omega)$. I want to obtain a real transformed function $h(t)$, which means that $H(-\omega)=H^{\ast}(\omega)$ has to be ...
6
votes
4answers
802 views

Why this gives 0?

fixed in 10.0.2. Why this gives 0? I am in shock, it should be Sinh[x]. FullSimplify[I InverseFourierTransform[FourierTransform[Cosh[t],t,w]/w,w,x]]
6
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2answers
401 views

Correct fourier scaling and high-resolution frequency identification

I have a dataset of amplitude versus time $(t,A(t))$ and I need to extract the dominant frequency and amplitude, and also get the amplitude at one other specific frequency. My data looks like this: ...
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0answers
67 views

problem using FourierTransform

I'd like to make a fourier transform of equation: ...
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0answers
74 views

Approximating The Fourier Transform

Eq.(1)$$f(z)=\frac {k}{2\pi}\int_{C}F(\theta)e^{ikz\cos \theta} \,d\theta$$ for $$|z|\le l$$ and the side condition Eq.(2) $$0=\frac {k}{2\pi}\int_{C}F(\theta)e^{ikz\cos \theta} \,d\theta$$ for ...
0
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0answers
25 views

How to keep computing Hilbert transforms until I find the right one

I would like to get mathematica to arbitrarily plug in pairs of functions to the Hilbert transform operation, and to stop as soon as it gives me a pair of Hilbert transforms that obey certain ...
1
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1answer
111 views

Trouble with Fourier transform of Exp[-Sqrt[x]]

First time trying to do something "real" in Mathematica, I am having trouble getting it to calculate this Fourier transform. It runs for a long time, then just prints the input expression. ...
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1answer
134 views

Why is my Fourier transformed matrix rotated?

After Fourier transforming and shifting the zero frequency of a matrix, my outcome is rotated by 45 degrees from what it should be. Can anybody spot why? ...
3
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1answer
81 views

How to create a 1D vector by selecting a straight line in a given angle of 2D array

Suppose I have an image created by the code provided below. I want to select a line (1D vector) $ \left(y-y_{0}\right)=n\left(x-x_{0}\right) $ from the output image (2D matrix) by specifying $n$ and ...
2
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1answer
136 views

2D Fourier transform of a few (4) disjoint discs on a plane

I'd really appreciate some advice. Short Version I'm trying to calculate the following $$ ...
2
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1answer
175 views

2-Dimensional NFourierTransform

Mathematica FourierSeries package contains the NFourierTransform function for calculating 1-D Fourier integral numerically. ...
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0answers
133 views

Mathematica does not calculate inverse fourier transformation or the convolution of two functions

I am trying to take convolution of a Gaussian function with an exponential function. Mathematica couldn't calculate it. ...
6
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1answer
267 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 ...
3
votes
4answers
534 views

Why does Fourier give a shifted frequency?

I have a signal that I want to identify the frequencies in it, I used the Fourier function but I can't get the frequency correctly. Here is a simplified example: ...
9
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0answers
338 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 ...
5
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1answer
234 views

Prove an identity in quantum harmonic oscillator

Problem: In the context of quantum harmonic oscillator the eigenfunctions are given by: $ u_n(x) = (N_n/\sqrt{b}) H_n(x/b) \exp\left[-x^2/(2b^2)\right] $, where $N_n$ is the normalization factor: $ ...
1
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0answers
64 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
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1answer
177 views

Programming a recursive FFT with Mathematica

I'm trying to program a FFT using a recursive function in Mathematica, though my program is not getting me anywhere at the moment. Could you say what's wrong with it and what I can do to make it work? ...
0
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1answer
112 views

How to set up the Fourier domain for a Fourier Transform? [duplicate]

I am having trouble understanding how to set up the grid in the Fourier domain, while performing Discrete Fourier Transforms. This might be a very trivial question, but I'd appreciate any help ...
0
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0answers
59 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 ...
3
votes
2answers
171 views

Fourier Analysis: How to get rid of a discontinuity

When I compute the phase error of a spatial series data using Fourier analysis in Mathematica there's a discontinuity @ parameter ...
6
votes
1answer
171 views

How to plot stability region of Fourier analysis

Stability limits for Runge–Kutta methods in the complex ΩΔt-plane are needed to be plotted like this: For example, let P=1+z where ...
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0answers
43 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 ...
3
votes
3answers
162 views

Fitting the Plot by fourier Series of either sine or cosine

I have list of data and its plot and I don't know how to fit the plot with fourier series of either sine or cosine. Full Data: ...
-1
votes
1answer
73 views

Ploting fourier transform [closed]

I want to Find the fourier transform of this graph. {ListLinePlot[hari, PlotRange -> {{0, 200000}, {-1.5, 1.8}}]} And when I Put: ListLinePlot[Abs[Fourier[hari][[2 ;; 100]]], PlotRange -> All, ...
0
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0answers
26 views

Why I am not getting the same frequency when sampling a waveform? [duplicate]

I am trying to simulate the sampling of a waveform to then apply FFT Analysis to it. Here is the sample code I have now using a square wave: ...
0
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0answers
70 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 ...
3
votes
2answers
222 views

Integration and Fourier transform

I would like to calculate the distribution function from the characteristic function. There is a formula given as $$F_X(x)=\frac{1}{2}+\frac{1}{2\pi}\int_{0}^\infty \frac{e^{i w x}\phi(-w)-e^{-i w ...