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

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74 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 ...
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0answers
40 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
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0answers
100 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 ...
2
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0answers
140 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 ...
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2answers
102 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
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0answers
218 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 ...
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0answers
56 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 ...
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2answers
268 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 ...
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0answers
41 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
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2answers
311 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. ...
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2answers
439 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
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1answer
345 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 ...
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1answer
94 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 ...
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0answers
49 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 ...
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1answer
196 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 ...
2
votes
1answer
263 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" ...
0
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1answer
218 views

Discrete Fourier Transform of a vector defined on a 3D lattice

In my research I need to compute the Discrete Fourier transform of a vector defined on a 3D lattice (a cube) to the "reciprocal" lattice. This is quite new to me so before proceeding i wanted to be ...
2
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0answers
50 views

Precision loss in FourierDCT

I have high precision data that I want to do Fourier transform with, but it looks like the precision is lost dramatically. ...
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0answers
326 views

Using 2D Fourier transform of an image to detect typical wavelengths

I am new to Mathematica, and I have read this post to understand how to perform Fourier transform on an image. My mission is to extract information on the typical distance between the black patches in ...
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0answers
123 views

The inverse Fourier transform of a rather complex function

I am using Mathematica 7.0 and trying to find the Fourier transform of a rather complex function g. The function g is defined by ...
5
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0answers
190 views

Periodogram for irregularly spaced data

I am trying to replicate some existing work on the length of the cycles in certain economic data. Specificially, I am using the Schularick and Taylor (2012) data set to replicate the periodogram shown ...
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0answers
145 views

Inverse Fourier transform not evaluating [on hold]

I'm trying to do this simple task: InverseFourierTransform[0.031622*Exp[0.4995 ω^2], ω, t] Mathematica 9.0 can't handle it for some reason (it returns with the ...
3
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1answer
282 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 ...
2
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1answer
120 views

Finding periodicity of multidimensional data?

I have a data set consisting of measurements of an $n$-dimensional vector $\mathbf{x}(t)$, at $N$ distinct time points $t_i$. The time points $t_i$ are equally spaced. I need to find the dominant ...
9
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2answers
244 views

InverseFourierTransform of simple function takes forever

i'm quite new to Mathematica. I'm trying to do something along the lines of: ...
2
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1answer
245 views

Is there any function in Wolfram Mathematica simmilar to fft.fftfreq (Python)

Here is an explanation of fft.fftfreq I have data with random noise: ...
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1answer
723 views

Discrete Fourier Transform with x axis data?

Usually, Fourier Transform in mathematica is supplied by y data only, like the famous Sin[x] transform example. What if my data is a list of ...
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0answers
31 views

Inverse Fourier transform to get real function [duplicate]

I have got a sampled complex function, $H(\omega)$ and know that its inverse Fourier transform has to be real function $h(t)$, which means that $H(-\omega)=H^{\ast}(\omega)$ has to be fulfilled. If we ...
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1answer
224 views

Inverse Fourier transform

I am dealing with an inverse Fourier transform of a sampled complex function, $H(\omega)$. I want to obtain a real transformed function $h(t)$, which means that $H(-\omega)=H^{\ast}(\omega)$ has to be ...
2
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1answer
309 views
3
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2answers
145 views

Compare two shifted signals

I have one set of original data (signal A) and a second set of derived data (signal B) which was computed from A by position rotation (circular shift). Here are the data for the signals (A and B): ...
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0answers
140 views

Can not understand the code to plot Fourier Series approximation of the line

I'm reading the CDF file from Making Formulas… for Everything in the WolframAlpha blog. I am confused by what's happening with In[9] and In[10]. Can anyone tell me what these two functions mean, or ...
1
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1answer
167 views

Trouble with Fourier transform of Exp[-Sqrt[x]]

First time trying to do something "real" in Mathematica, I am having trouble getting it to calculate this Fourier transform. It runs for a long time, then just prints the input expression. ...
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1answer
199 views

Why is my Fourier transformed matrix rotated?

After Fourier transforming and shifting the zero frequency of a matrix, my outcome is rotated by 45 degrees from what it should be. Can anybody spot why? ...
3
votes
1answer
146 views

How to create a 1D vector by selecting a straight line in a given angle of 2D array

Suppose I have an image created by the code provided below. I want to select a line (1D vector) $ \left(y-y_{0}\right)=n\left(x-x_{0}\right) $ from the output image (2D matrix) by specifying $n$ and ...
2
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1answer
193 views

2D Fourier transform of a few (4) disjoint discs on a plane

I'd really appreciate some advice. Short Version I'm trying to calculate the following $$ ...
6
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4answers
855 views

Why this gives 0?

fixed in 10.0.2. Why this gives 0? I am in shock, it should be Sinh[x]. FullSimplify[I InverseFourierTransform[FourierTransform[Cosh[t],t,w]/w,w,x]]
2
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1answer
267 views

2-Dimensional NFourierTransform

Mathematica FourierSeries package contains the NFourierTransform function for calculating 1-D Fourier integral numerically. ...
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0answers
259 views

Mathematica does not calculate inverse fourier transformation or the convolution of two functions

I am trying to take convolution of a Gaussian function with an exponential function. Mathematica couldn't calculate it. ...
2
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0answers
100 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 ...
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0answers
86 views

Fourier transform an expression to obtain a distribution?

I have this expression for the correlation function for a rigid rotating molecule: $G(\tau) = 4 \pi \int \omega ^2 P_2[\cos (\omega \tau)] P(\omega) \, \mathrm{d}\omega \quad [1]$ where $P_2$ is a ...
1
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1answer
258 views

How to set up the Fourier domain for a Fourier Transform? [duplicate]

I am having trouble understanding how to set up the grid in the Fourier domain, while performing Discrete Fourier Transforms. This might be a very trivial question, but I'd appreciate any help ...
1
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0answers
109 views

Issues with zero frequency component in discrete Fourier transform [closed]

I'm having trouble with the Fourier function at the moment. I'm solving a set of differential equations with NDSolve, then need to extract the spectrum associated with the curve below: So i use ...
4
votes
1answer
237 views

Programming a recursive FFT with Mathematica

I'm trying to program a FFT using a recursive function in Mathematica, though my program is not getting me anywhere at the moment. Could you say what's wrong with it and what I can do to make it work? ...
6
votes
1answer
307 views

How to plot stability region of Fourier analysis

Stability limits for Runge–Kutta methods in the complex ΩΔt-plane are needed to be plotted like this: For example, let P=1+z where ...
3
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2answers
255 views

Fourier Analysis: How to get rid of a discontinuity

When I compute the phase error of a spatial series data using Fourier analysis in Mathematica there's a discontinuity @ parameter ...
9
votes
1answer
174 views

Workarounds for a possible bug in the linearity of FourierTransform

This is somewhat similar to this question, except the problem I am encountering is to do with Fourier transforms of scalar multiples of functions and their derivatives. I wish to input ...
4
votes
4answers
778 views

Why does Fourier give a shifted frequency?

I have a signal that I want to identify the frequencies in it, I used the Fourier function but I can't get the frequency correctly. Here is a simplified example: ...
3
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3answers
255 views

Fitting the Plot by fourier Series of either sine or cosine

I have list of data and its plot and I don't know how to fit the plot with fourier series of either sine or cosine. Full Data: ...
0
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0answers
31 views

Why I am not getting the same frequency when sampling a waveform? [duplicate]

I am trying to simulate the sampling of a waveform to then apply FFT Analysis to it. Here is the sample code I have now using a square wave: ...