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

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5
votes
2answers
151 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
57 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
218 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. ...
10
votes
1answer
187 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 ...
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
42 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
42 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
41 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
78 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
91 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
453 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
79 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 ...
0
votes
0answers
30 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
110 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
12 views

Create periodic function from combining non-periodic functions [migrated]

I'm studying recurrent neural networks which often use tanh as an activator function which is not periodic. However in research and papers it's shown that these recurrent neural nets can exhibit ...
0
votes
0answers
26 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 ...
12
votes
3answers
496 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
160 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 ...
14
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
220 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
46 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
85 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
37 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
93 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 ...
0
votes
1answer
79 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
votes
1answer
89 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
votes
0answers
43 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. ...
3
votes
2answers
124 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): ...
0
votes
0answers
80 views

How to filter my signal?

As you can see, my signal is superimposed by an other sinus which has a slightly longer frequency. I would like to filter this out. I think I can do the filtering process, but there is one step that I ...
1
vote
0answers
144 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 ...
0
votes
0answers
90 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
votes
0answers
145 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 ...
4
votes
1answer
121 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 ...
1
vote
0answers
107 views

Inverse Fourier Transform - wolfram alpha vs Mathematica 9.0

I'm facing an interesting problem. I'm trying to do this simple task: InverseFourierTransform[0.031622*Exp[0.4995ω^2], ω, t] Mathematica can't handle it for some ...
0
votes
0answers
88 views

Fourier Transformation of a List

As we know the FourierTransform goes a function of t ,for example, f[t] to ...
9
votes
2answers
215 views

InverseFourierTransform of simple function takes forever

i'm quite new to Mathematica. I'm trying to do something along the lines of: ...
2
votes
1answer
99 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 ...
2
votes
1answer
153 views
1
vote
1answer
263 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 ...
0
votes
0answers
26 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 ...
1
vote
1answer
147 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 ...
6
votes
4answers
816 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]]
6
votes
2answers
454 views

Correct fourier scaling and high-resolution frequency identification

I have a dataset of amplitude versus time $(t,A(t))$ and I need to extract the dominant frequency and amplitude, and also get the amplitude at one other specific frequency. My data looks like this: ...
0
votes
0answers
77 views

problem using FourierTransform

I'd like to make a fourier transform of equation: ...
0
votes
0answers
81 views

Approximating The Fourier Transform

Eq.(1)$$f(z)=\frac {k}{2\pi}\int_{C}F(\theta)e^{ikz\cos \theta} \,d\theta$$ for $$|z|\le l$$ and the side condition Eq.(2) $$0=\frac {k}{2\pi}\int_{C}F(\theta)e^{ikz\cos \theta} \,d\theta$$ for ...
0
votes
0answers
28 views

How to keep computing Hilbert transforms until I find the right one

I would like to get mathematica to arbitrarily plug in pairs of functions to the Hilbert transform operation, and to stop as soon as it gives me a pair of Hilbert transforms that obey certain ...
1
vote
1answer
126 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. ...
0
votes
1answer
154 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? ...