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

learn more… | top users | synonyms

0
votes
1answer
81 views

Discrete Fourier Transformation

Assuming I have a function $f(x)$. I can use a numerical Fourier transformation: NFourierTransform[] to find some points of $F(\omega)$. How can I do the same ...
11
votes
1answer
320 views

How can I use Mathematica to numerically compute a Wigner spectrogram of an optical pulse?

This question was inspired by this question where it is necessary to numerically compute the Fourier transform of a Gaussian optical pulse with a Gaussian chirp function. $$E(t)=e^{-t^2} \cos(50 t - ...
17
votes
3answers
2k views

How to calculate the Fourier Transform of a Gaussian pulse with a nonlinear chirp: Cos[ t + Exp[t^2] ]?

I have an optical pulse in time domain: Exp[-t^2] Cos[50 t - Exp[-2 t^2] 8 π]. The figure of this formula is I hope to calculate the Fourier Transform of ...
1
vote
2answers
112 views

Parseval identity in one side Fourier Transform

Is there any posibility to apply Parseval identity(energy in time domain is equal to freq. domain) on One/Single-side Fourier transform? In other word for "standard" FT the test Mathematica can be <...
1
vote
2answers
189 views

How do I extract peak frequencies? [closed]

Suppose I have large text file filled with numerical data. Then I do Fourier operation with this file and plot the result: ...
9
votes
1answer
168 views

How can I make FourierCoefficient et al. handle the zero-order term correctly?

Say that I would like to use Mathematica to step through one of the most famous solutions to the Basel Problem, using Parseval's Identity, $$ \sum_{n = -\infty}^\infty \left|c_n\right|^2 = \frac{1}{2\...
-2
votes
1answer
115 views

A piecewise function with way too many pieces

I'm currently calculating a periodic square wave current function to feed into a particle accelerator. It's a square wave that ramps up to a certain frequency and then drops back to the base frequency ...
2
votes
1answer
51 views

TrigExpand-ing too far

Something simple: I'd like TrigExpand[Sin[3n-3]] to return Sin[3n]Cos[3]-Cos[3n]Sin[3] instead of ...
0
votes
0answers
253 views

Normalization of discrete Fourier transform not obvious

I'm trying to write some code (eventually in Fortran) to quickly calculate the Voigt profile using the convolution theorem. However, I ran into some trouble using the Intel MKL FFT library, so I'm ...
2
votes
0answers
59 views

How do I let Fourier Transform know that it is a linear operator? [duplicate]

I have the following issue with FourierTransform, Fourier transform doesn't seem to know it is a linear operator. ...
1
vote
0answers
102 views

Assumptions don't work as expected in FourierTransform

The 2D rectangular function and its Fourier Transform is $$ g_{in}(x,\,y) = rect(\frac{x}{x0}) \, rect(\frac{y}{y0}) \quad \xrightarrow{\mathscr{F}} \quad G_{in}(u,v) = x0 \, y0 \, sinc(\pi u x0) \, ...
0
votes
2answers
153 views

Wrong frequency in Fourier

I have a file, filled with data like this: As you can see the approximate frequency is about $5/1000 = 0.005$, then angular frequency is about $2 \pi \times 0.005 \approx 0.03$. Then I use discrete ...
1
vote
2answers
89 views

DataRange in plotting Fourier

I'm trying to estimate a frequency spectrum of a given discrete function. I have a file which is filled of values of Sine-function $sin(t)$, where $t$ runs from $0.0$ to $100.0$ and a discrete step is ...
6
votes
1answer
581 views

Angle between two areas of an image of a 2D FFT

I'm trying to obtain the angle between the red line and the area surrounded by the red circle, related to the middle of the image. Usually the area surrounded by the red circle is lighter than the ...
1
vote
1answer
56 views

NIntegrate option for FourierSeries

I would like to use FourierSeries but it is very slow. My guess is that it is because it uses symbolic integration: ...
3
votes
0answers
99 views

Using NIntegrate and DiscretePlot to visualize pseudodifferential operators

In harmonic analysis, pseudodifferential operators are a way to generalize the notions of derivatives, through the use of Fourier transforms. The basic idea being, Let $u(x)\in\mathcal{S}(\mathbb{R}^...
5
votes
1answer
444 views

2D Fourier transform

I want to calculate the 2D Fourier transformation of a circular shaped aperture, but Mathematica won't finish the calculation: ...
1
vote
0answers
89 views

Perform a Fourier Transform on a wavelength scan

I have a plot of the power transmitted through a device as a function of wavelength, from 1500 to 1600nm. There is some Fabry-Perot noise, plus I suspect some other regularities. I would like to ...
1
vote
0answers
56 views

Discrepancy between laplace and fourier transform of gaussian

The function in question is Exp[x^2/2] for x>0 Laplace transform should be the same as the fourier transform since the function is absolutely integrable. Fourier: They are indeed the same ...
3
votes
0answers
85 views

Analytical Fourier Transforms with convolution rule [closed]

The task is the following, how to extend Mathematica's FourierTransform command in order to be able to analytically deal with non-linear differential equations. To do so it should be able to deal with ...
4
votes
1answer
271 views

Averaging over a circle from FFT to plot the amplitude vs wavelength

I am trying to calculate the amplitude of FFT vs wavelength for some experiments. I had put a question here previously on how to compute the FFT of an image. Thanks to everyone who provided the ...
3
votes
1answer
68 views

Fourier cosine series of displacement

I'm trying to calculate a Fourier Cosine Series of displacement for general 4-bar mechanism. My code not working. I don't understand why. I need the result as this form ...
5
votes
1answer
542 views

Find a Fourier series from discrete data

I am trying to fit a Fourier cosine series to discrete data. I read through this, but I was not able to understand it. The data should be periodic with a period of $0.2 \text{ m}$, and it is the ...
2
votes
0answers
50 views

FourierTransform of a gaussian at -1 and 2

Let ft[w_] := FourierTransform[Exp[-t^2], t, w] Then ft[#] & /@ Range[-2, 3] Evaluates to ...
7
votes
1answer
746 views

Calculation of 2D FFT for an image

I am trying to obtain 2D FFT of an image. From the 2D FFT, I wish to calculate the amplitude of the FFT averaged over a circle vs the distance in pixels by varying the radius of the pixels which is ...
1
vote
1answer
249 views

How to solve time dependent coupled differential equations using Floquet method?

I have coupled differential equations D[X[t], t] == M[t] X[t] + R[t] where ...
1
vote
0answers
71 views

Discrete Fourier Transform baseline subtraction

I am trying to remove sinusoidal variability from a set of evenly-spaced intensity vs. time data. These data contain periodic events that are separated by a normalized (but sinusoidally variable) ...
1
vote
1answer
119 views

Strange behavior of `FourierSinCoefficient`

FourierSinCoefficient works normally like this and the result is checked with Integrate. ...
0
votes
1answer
139 views

Fourier series of the odd extension of a function [duplicate]

Using Mathematica to make a plot, I noticed that the interval it's defined over must be changed in order to do the Fourier series. How do I change the interval to be on an interval of $[-{\cal l}, {\...
1
vote
1answer
243 views

DFT: why are frequencies mirrored around the frequency axis?

I want to apply Mathematica's DFT procedure, Fourier[], to a Gaussian. Why a Gaussian? Because I know the analytical result. So I define ...
3
votes
1answer
474 views

Differences between FFT and analytical Fourier Transform

In MATLAB, if I perform an FFT on a simple Gaussian spot with a phase grating: ...
1
vote
1answer
108 views

Problem of Discrete Fourier?

I tried Fourier Transform for a range of figures. Firstly, I tried in this way. ...
7
votes
1answer
1k views

What do the X and Y axis stand for in the Fourier transform domain?

In Wolfram Mathematica the function Fourier has the following declaration Fourier[list] And after a list is given to the ...
0
votes
0answers
71 views

3-adic FFT algorithm

I am trying to implement the FFT algorithm when $n=3^k$, but maybe my code is wrong. Are there any suggestions for improving my code? ...
1
vote
1answer
164 views

Finding the discrete Fourier transform for a simple oscillator?

Here's what I want to do, initially at least: I have an oscillator, it's in some force field, I've integrated it using the Euler method, so I have a list of points of the form {t,x}, where t is the ...
1
vote
1answer
224 views

Precision while calculating Fourier transform

I'm trying to understand how precision works in Mathematica. Particularly I'm calculating discrete Fourier transform using the Fourier function and calculating it "...
1
vote
0answers
71 views

Monitor Progress of a function (Fourier[] in my case)

I am using PSD = Abs[Fourier[normedAutoValues, FourierParameters -> {-1, 1}]]; normedAutoValues contains around 200 *10^7 ...
6
votes
2answers
356 views

Filtering of an unwanted frequency through a Fourier Transform

I have a data set with evenly spaced data points. The plot is frequency vs. intensity. The overall shape of the plot is an upwards curve into a plateau, this cannot be seen in the data as this is an ...
0
votes
0answers
41 views

InverseFourier of nested lists

last week I've got an Mathematica package that is using several inverse Fourier transforms on a data cube ($n\times n\times n$-array). I'm implementing the same functionality in C++ and tried to ...
3
votes
0answers
147 views

Different FourierParameters in each dimension for discrete Fourier transform

I have a query about the Fourier utility, that does discrete Fourier transforms. I am unable to find any information on whether different FourierParameters can be used in each dimension. This is a ...
3
votes
0answers
199 views

Calling CUDA cuFFT

Following ybeltukov's excellent answers (see here and here) about how to access the CUDA library functions and interact with Mathematica through CUDAMemory, I tried to compile the code given in ...
1
vote
2answers
111 views

Why does InverseFourierTransform gives different result to doing it by hand?

When I can calculate an inverse fourier transform by the built-in function InverserFourierTransform, the result is different from what I calculate by definition ...
4
votes
0answers
309 views

Help with Fourier analysis and filtering of an image

I am starting with the following image: For the curious, it is an STM scanned image of graphite. I am hoping to find some kind of periodic structure in the image related to the honeycomb structure ...
1
vote
0answers
66 views

PeriodogramArray or PowerSpectralDensity?

could anyone explain what is the difference between PowerSpectralDensity[data,omega] and PeriodogramArray[data]? When I plot them (starting from the same set of data of course) I get two different ...
1
vote
2answers
364 views

Get Y-Axis of FFT in decibels

I am trying to make a plot of a sound file similar to Audacity's FFT plot which looks like this when the x-axis is on a log scale: My plot of the same sound file (below) has the problem that the ...
0
votes
0answers
49 views

FourierSinCoefficients extremely slow

I'm just playing with Fourier decomposition of periodic functions. We had a similar example with standing waves and cosines in class, so I tried to expand a triangle wave in sines. This is what I came ...
2
votes
2answers
371 views

Using Periodogram to investigate the seasonality of the data

After asking how to get rid of the seasonality of this set of data, I'd like to ask how to investigate the seasonality in data using Mathematica. Which tool would you use to study seasonality? I.e. ...
1
vote
2answers
588 views

How to calculate the phase spectrum

I have the following frequency characteristics in the Fourier domain: $$H(\omega)=\frac{-\omega^2}{63170s^{-2}-\omega^2+355.1s^{-1}i\omega}$$ How do I find the phase spectrum from this? I should ...
4
votes
1answer
439 views

Finding the dominant frequency in a large dataset with Fourier + periodogramm

I know there are dozens of questions about how to extract the correct frequency out of data, however I probably don't interpret my data correctly, or do not apply those answers correctly. Problem I ...