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

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12
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1answer
2k views

Computation of Hankel Transform using FFT (Fourier)

To address circularly symmetric cases of 2-D Fourier Transformations, the so-called Hankel Transform can be applied (for a detailed derivation of the relation between the 2-D Fourier transform and the ...
1
vote
0answers
35 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 ...
11
votes
1answer
411 views

Inconsistent results of second derivative of inverse fourier transform

Bug introduced in 9.0 or earlier and persisting through 10.2.0 I am trying to get the Green's function of a toy diffusion equation $$\frac{\partial^2 u(x,t)}{\partial x^2} = ...
0
votes
1answer
71 views

Strange behavior of `FourierSinCoefficient`

FourierSinCoefficient works normally like this and the result is checked with Integrate. ...
3
votes
0answers
31 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
78 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
54 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 ...
10
votes
5answers
2k views

How do you find the frequency and amplitude from Fourier?

The problem is that a typical harmonic time history will not have an integer number of cycles in the data. For example, with the following time history you get a numerical Fourier transform. ...
4
votes
1answer
152 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. This data should be periodic with a period of $0.2 \textrm{m}$ and it is the ...
2
votes
0answers
46 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 ...
1
vote
1answer
131 views
6
votes
1answer
151 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
0answers
42 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) ...
0
votes
1answer
64 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}, ...
5
votes
2answers
866 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, ...
1
vote
1answer
110 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 ...
10
votes
1answer
208 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 ...
7
votes
0answers
150 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
0answers
88 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
80 views

Problem of Discrete Fourier?

I tried Fourier Transform for a range of figures. Firstly, I tried in this way. ...
4
votes
1answer
145 views

What do the X and Y axis stand for in the Fourier Transformation in wolfram mathematica?

In wolfram mathematica the function Fourier has the following declaration Fourier[list] And after a list is given to the function, a simple Plot gives the ...
0
votes
0answers
55 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
84 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
123 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
52 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 ...
3
votes
1answer
239 views

Approximate $h$ in $F(\theta)=\sin \theta \int_{-L}^{+L}h(z)e^{-ikz\cos \theta} \,dz$

Consider $$F(\theta)=\sin \theta \int_{-L}^{+L}h(z)e^{-ikz\cos \theta} \,dz$$ $$|z|\le L$$ $$0 \le \theta \le \pi$$ By having knowledge of $F(\theta)$, how can one approximate $h(z)$? In ...
6
votes
2answers
172 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
66 views

Using Fourier to return exponential function

I am trying to use Fourier to numerically demonstrate the following identity: $$ \frac{1}{2\pi}\int_{-\infty}^{\infty}\frac{e^{i\,s\,y}}{1 + a\,s}ds=e^{-y/a} $$ I'm getting the correct shapes, but my ...
2
votes
2answers
257 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. ...
0
votes
0answers
30 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
55 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 ...
0
votes
0answers
46 views

How to change the period in FourierSeries

I have a function that represents a 9-bit transmission and gives one cycle of periodic signal. I need to plot it for three different frequencies, How can I change the cycle time from $[-\pi, \pi]$ to ...
2
votes
0answers
81 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
83 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 ...
0
votes
0answers
158 views

fourier frequency analysis for NDSolve of complex variable

i have a set of coupled equations for complex amplitudes c1 and c2, for which i'd like to find frequency and phases (and phase shift); i looked up for some nswers on the forum, but can't seem to find ...
3
votes
1answer
484 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 ...
3
votes
0answers
103 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
38 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
145 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
30 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 ...
13
votes
3answers
518 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. ...
4
votes
1answer
200 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 ...
15
votes
1answer
2k views

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

I'm trying to apply a Fourier transform of a one dimensional list of a time history of some quantity using the Fourier function. I'm interested in the frequency ...
1
vote
2answers
255 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 ...
1
vote
1answer
62 views

Changing Function Domain of Fourier Series

If I write FourierSinSeries[x, x, 10] Mathematica will output the first 10 terms of the Fourier Sine Series f(x) = x defined for 0 < x < Pi. How do I output the the Fourier Sine Series for ...
11
votes
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, ...
1
vote
0answers
93 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
votes
0answers
39 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 ...
1
vote
1answer
113 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 ...
1
vote
1answer
98 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" ...