# Tagged Questions

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

1answer
76 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)) ...
1answer
75 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 ...
1answer
280 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 ...
1answer
87 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 ...
1answer
65 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 ...
1answer
160 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 ...
0answers
205 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 ...
2answers
167 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, ...
1answer
121 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 ...
0answers
108 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 ...
2answers
226 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, ...
0answers
72 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 ...
0answers
104 views

### Finding Peaks in an Image using Fourier — Problems with Derivatives

Rest of OP is below, but I am editing to add that the real problem seems to be in the way my functions are being defined. Sorry, but the one reply below is not clear enough to help here. My function ...
1answer
158 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: ...
1answer
525 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 ...
1answer
270 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 ...
2answers
304 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 ...
1answer
270 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 ...
0answers
279 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 ...
2answers
321 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 ...
0answers
141 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 ...
0answers
237 views

### Mathematica's definition of Fourier Transform

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 ...
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 ...
1answer
403 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 ...
2answers
763 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 ...
2answers
482 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 ...
2answers
156 views

### Speed up Fourier for Booleans

I'm calculating a bit of the power spectrum of a two color cellular automaton using: ...
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} ...
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 ...
2answers
232 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 ...
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. ...
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 ...
2answers
2k views

### 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.
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