Tagged Questions

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

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10
votes
2answers
1k views

Finding fourier transform of data and hence frequencies

I looked at all the other questions related to mine before posting this, and they didn't solve my problem. I have a large data set which can be downloaded from here. I'm using the following code to ...
2
votes
1answer
236 views

Integrate message: can't prove Integration limits are real

I'm working on solving differential equations through Fourier series, I made a function to help me calculate the coefficients that looks like this: ...
1
vote
1answer
75 views

Two dimensional NIntegration failure - non-numerical values

I've got this function: E0[x0_, y0_, z_]:= A/w[z]*Exp[-(x0^2 + y0^2)/(w[z]*w[z])]*Exp[(I*2*Pi*(x0^2 + y0^2))/(λ*2*R[z])]*Exp[I*ϕ[z]]; Where the ...
0
votes
1answer
116 views

Fourier-Analysis How to display every period correctly? [duplicate]

I want to express a function as a sum of fourier series. I tried the code below. It works. But only get one period (from 0 to 1). How to display every period correctly? ...
2
votes
1answer
167 views

Why does FourierTransform[] converge while same integral manually written does not?

I'm studying the quantum mechanics of an infinite square well from a computational standpoint. My eigenfunctions are defined as $u_n(x)=\sqrt{2/L}\sin\left(n\pi x/L\right),\quad 0 \le x \le L, \quad ...
3
votes
3answers
95 views

Filling in explicit zeros in a (x,y) list for nonexisting y values for discrete Fourier transform in Mathematica

I have a list of (x,y) values in Mathematica for various discrete x values, as in ...
0
votes
1answer
85 views

Is there a way to plot discrete functions in mathematica? [closed]

Suppose you have a discrete function Triangle[n/5]. How would you plot it in mathetica?
2
votes
1answer
239 views

Animated Wave Propagation using Fourier & InverseFourier

This is a continuation off of previous help on the first part of my project: fourier issue arising from input miscommunication Now I want to go one step further in the current code. Here's the code ...
0
votes
2answers
93 views

fourier issue arising from input miscommunication

xdomain = Table[i , {i, -10, 10, .1}]; ListPlot[InverseFourier[ Fourier[E^-#^2 & /@ xdomain]*E^#^2 & /@ xdomain]] So I want to numerically fourier ...
5
votes
0answers
115 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 ...
0
votes
1answer
213 views

Plotting partial sums of Fourier sine series

How do I plot this on Mathematica version 5.2? $\frac{4}{\pi} \sin{x} + \frac{4}{3 \pi} \sin{3 x} + \cdots + \frac{4}{(2 N+1) \pi} \sin{(2 N+1) x}$ over $x \in [-\pi,\pi]$ for $N= 3, 6, 12, 24$. I ...
10
votes
1answer
934 views

What's the correct way to shift zero frequency to the center of a Fourier Transform?

I'm trying to Fourier transform a one dimensional list of a time history of some quantity using the Fourier function. I'm interested in the frequency spectrum, but ...
6
votes
2answers
599 views

Band-pass filter an image

Ok so i have some HR-TEM images. In this technique fringes appear whereever a crystalline structure is present. This fringes are separated by a certain distance depending on the material, this is our ...
4
votes
2answers
575 views

Frequencies represented in a DFT list (Fourier[])

I have a sound sample (sample rate: 44100). When I have a list l with n successive elements from the sample, ...
10
votes
1answer
386 views

Why does Mathematica return a Fourier transform for a function for which it is not defined?

The following function $$g(x) = (1 + x^{1/a} )^a $$ should NOT have a Fourier transform, as far as I am aware, for any real values of $a$ since $g(x)$ is not nice in the sense of decays quickly ...
5
votes
2answers
587 views

How to draw a graph about the FourierTransform of a 2D Function?

Here is a 2D function, and it cannot be calculated by the FourierTransfrom ...
6
votes
0answers
141 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 ...
8
votes
2answers
428 views

Why Fourier doesn't show me the peaks?

I'm trying to identify the frequencies in my time history samples, and I can see a frequency in the time history, but can't see it in its Fourier transform. Here it is : the sample data: ...
1
vote
1answer
331 views

Problem with Fourier and InverseFourier function

I have the following code Image[img, ImageSize -> 300] data = ImageData[img]; fdct = Fourier[data] tdata = InverseFourier[fdct]; Image[tdata] but it seems to ...
-5
votes
1answer
2k views

Determine the 2D-Fourier transform of an Image

I am new to Mathematica and using Version 8.0. I want to calculate the 2D-Fourier Transform of a digital image and see its Magnitude and Phase Spectrum, and reconstruct it.
9
votes
1answer
566 views

FourierTransform and Partial Derivatives?

I have a function of three variables $f(x,y,z)$, and it obeys a linear partial differential equation. I'm checking my by-hand calculations with Mathematica. I want to convert the PDE into the ...
8
votes
2answers
388 views

Next highly composite number?

R language has this function 'nextn' (link) which computes the next highly composite number greater than a given one, which is used to find the optimal padding size for the subsequent FFT operation. ...
16
votes
4answers
916 views

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 ...
9
votes
1answer
1k 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
1answer
99 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)) ...
0
votes
1answer
270 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 ...
9
votes
1answer
412 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 ...
2
votes
1answer
680 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 ...
0
votes
1answer
149 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 ...
1
vote
0answers
431 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 ...
1
vote
2answers
1k 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
550 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 ...
8
votes
2answers
1k 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, ...
1
vote
1answer
418 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: ...
9
votes
2answers
5k 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 ...
12
votes
1answer
487 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 ...
2
votes
2answers
920 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 ...
7
votes
1answer
525 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 ...
2
votes
0answers
302 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
743 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 ...
9
votes
0answers
320 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 ...
7
votes
2answers
2k views

Fourier Transform of a Step Function

I'm trying to obtain the form of a sinc function that I know I'm supposed to get in Mathematica. I'm doing this because I intend to do a lot with Fourier transforms (FT) and I'd like to know I'm not ...
1
vote
1answer
895 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 ...
20
votes
2answers
2k 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 ...
1
vote
2answers
1k 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 ...
7
votes
2answers
192 views

Speed up Fourier for Booleans

I'm calculating a bit of the power spectrum of a two color cellular automaton using: ...
12
votes
1answer
3k 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} ...
18
votes
3answers
2k 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
2answers
281 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 ...
8
votes
3answers
4k 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. ...