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

learn more… | top users | synonyms

0
votes
0answers
52 views

Fourier-style solutions to differential equations, not piecewise polynomials

NDSolve returns piecewise polynomials. Is there any way I can get a single (non piecewise) function consisting of sines and cosines instead? Sort of a "Fourier approximation" to the solution of my ...
0
votes
1answer
63 views

Discrete Fourier Transform: help on how to convert x axis in to the frequency when I have a set of data samples [duplicate]

I have a huge data set (400000 sample) and when I plot them ListLinePlot[Au4, PlotRange -> {All, All}] I used the following code to Fourier transform it ...
2
votes
0answers
72 views

How to do the Fourier transform of a picture? [duplicate]

I want to generate Fourier transforms of a picture. the transform can represent the diffraction pattern of the picture. Basically, if I have a picture. Then, the result should look like this: For ...
4
votes
1answer
96 views

Using 2 D FFT for filtering unwanted texture on an image

I have an image that spurious waves texture appears: I want to use 2D FFT to remove this texture, so I applied the following code from Calculation of 2D FFT for an image : ...
0
votes
1answer
55 views

Lack of precision in solar declination leads to odd Fourier result

Here's the sun's declination for a 10 year period (roughly 2000-2010): ...
3
votes
2answers
94 views

Discrete Fourier Transform - Inadequate precision and wrong peak positions

I have a small problem with a piece of code. I searched the site but was not able to find an answer to my specific question. I am trying a quick test of the Fourier capabilities (on lists) of ...
3
votes
1answer
84 views

Why the Spectrogram can't plot correctly?

The same data lead two different graph. Plot[E^(-Pi*(t - 5)^2), {t, -10, 10}, PlotRange -> All] The method to plot the spectrogram use the build-in ...
4
votes
1answer
98 views

Phase in discrete Fourier transformation [duplicate]

I asked a question some days ago and it was very well answer. However, I have a new one. I don't understand why the phase of the discrete fourier transformation is not correct. It has the correct ...
2
votes
1answer
65 views

Reconstruct signal using InverseFourier [closed]

I start from a signal, I do discrete Fourier transform of the signal, and I want to get back this same signal doing a discrete inverse Fourier transform. However, when I do so, I do not obtain the ...
2
votes
0answers
49 views

How can I analyse and manipulate k-space data of a DICOM imageset? [closed]

I'm very new to Mathematica. I've some MRI images as 3D DICOM data. I want to get the corresponding k-space data to identify all the signals with their corresponding amplitude, frequency and phase. ...
0
votes
1answer
75 views

Fourier Series and epicycles - How to find the radii and angular velocities from a function's Fourier Series expansion

The following code is a bit clumsy, but it constructs a variable number (n) of epicycles using the values from the radii and angularVel tables that follows the path of a parametric given as a sum of ...
0
votes
1answer
68 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
226 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 - ...
15
votes
3answers
1k 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
89 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
149 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
159 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 = ...
-2
votes
1answer
87 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
135 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
57 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
80 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
117 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
73 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
491 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
48 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
90 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 ...
5
votes
1answer
230 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
72 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
46 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
65 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
189 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
63 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
367 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
49 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
461 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
196 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
59 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
114 views

Strange behavior of `FourierSinCoefficient`

FourierSinCoefficient works normally like this and the result is checked with Integrate. ...
0
votes
1answer
101 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
167 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
254 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
98 views

Problem of Discrete Fourier?

I tried Fourier Transform for a range of figures. Firstly, I tried in this way. ...
6
votes
1answer
585 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
66 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
127 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
182 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 ...
0
votes
0answers
62 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
250 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 ...