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

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3
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2answers
164 views
1
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1answer
129 views

Image Filtering in the frequency domain

Here is a good starting to fiter image in the frequency domain lena = ColorSeparate[ImageResize[ExampleData[{"TestImage", "Lena"}],{121,121}]][[1]]; (Create a ...
3
votes
1answer
224 views

Why doesn't Mathematica evaluate FourierTransform[Exp[-t], t, w]?

I am having trouble getting Mathematica to evaluate a trivial Fourier transform. I would like to be able to evaluate the Fourier transform of the right-sided exponential decay function as shown ...
1
vote
1answer
93 views

Fourier transformation of multidimensional list [closed]

x is a list containing 7 trajectories (Dimensions[x] = {2726, 7}) of which I want to calculate the FFT. ...
2
votes
1answer
39 views

FourierTransform a function doesn't give result when variable is 0

I am trying to get a Fourier Transform of a function. However it doesn' work when the variable is 0. I used Mathematica 8.0 on a Windows Server 2008 R2 system. The code is as follows: Defining ...
4
votes
0answers
106 views

Fourier transform of Exp[x]/x

Could you please explain why Mathematica gives the following expression when taking Fourier transform of $\exp(\lambda z)/\lambda$? $$\frac{-\log(-z)+\log(z)}{\sqrt{2\pi}}$$ Why the answer does not ...
1
vote
2answers
48 views

FourierSeries command , for arbitrary period T?

ExptoTrig[FourierSeries[Piecewise[{{-Pi,-2Pi<x<=0},{Pi,0<x<=2Pi}}],x,3]] You can see, the function goes from $(-2\pi,2\pi]$ But Wolfram Alpha gives a ...
2
votes
3answers
465 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 ...
10
votes
1answer
246 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 ...
0
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0answers
86 views

FourierTransform a differental-equations [duplicate]

I want to use the command FourierTransform to transform a differential equations from time - domain to complex frequency domain but it don't works. My code is ...
3
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0answers
85 views

Computation of a Fresnel Diffraction pattern with Discrete Hankel Transform

In the next link: Computation of Hankel Transform using FFT (Fourier) Rainer implemented a great solution given in the next reference: Manuel Guizar-Sicairos and Julio C. Gutiérrez-Vega, "Computation ...
15
votes
1answer
595 views

How to use 2D Fourier analysis to clean the noise in an image

I have some other method to do this.But I desire to know how to use Fourier analysis to realize it. I found a base post about Fourier-analysis to use in Image-Processing--Calculate the 2D Fourier ...
14
votes
1answer
3k 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 ...
3
votes
1answer
75 views

Find the function $f(x)$ by using its fourier expansion

It is easy to find the fourier coefficient and fourier expansion of $f(x)$ function. But I want solve the inverse problem by using Mathematica How to find the function $f(x)$, if I know its ...
0
votes
1answer
62 views

How to use a Fourier-transform on variable which is multiplied by a constant

I have tried to do this calculation: ℏ := 1.05457168*10^-34 FourierTransform [ψ[x], x, ℏ*p] but the result is: How can I do it right?
2
votes
1answer
49 views

What is the correct way to represent this sum?

The summation of Fourier series of Sin[x-x[i]] at three location x[1] to x[3] is: ...
0
votes
1answer
50 views

Inverse of a Fourier matrix [closed]

I am trying to find the inverse of a Fourier matrix but I am getting confusing results. If R is a Fourier matrix, then ...
3
votes
2answers
104 views

Why do I encounter 1/0 expression

I am trying to write my periodical function $f(t)$ in Fourier Series $$f(t)=\frac{a_0}{2}+\sum_{j=1}^Na_j\cos(j 2\pi t/\tau)+\sum_{j=1}^Nb_j\sin(j 2\pi t/\tau)$$ and I know that there is a really nice ...
2
votes
0answers
74 views

FourierCoefficient performance

I encountered weird performance issue while using FourierCoefficient[]. I narrowed it down to calculating $n$-th coefficient for $\cos(nx)$. ...
2
votes
2answers
7k views

Calculate the 2D Fourier transform of an Image

I am new to Mathematica, and using version 8.0. I would like to calculate the 2D Fourier Transform of an Image with Mathematica and plot the magnitude and phase ...
1
vote
1answer
71 views

How are Fourier transformations calculated?

Lets say my function is $$f(t)=\left\{\begin{matrix} 1 &, -T_p/2\leq t \leq T_p/2\\ 0& , |t|>T_p/2 \end{matrix}\right.$$ than a Fourier transformation is calculated $$F(j\omega)=\int_{-\...
1
vote
1answer
96 views

Plotting a periodic function [duplicate]

My question is the following: how can I plot a function repeatedly? By following some topics here I found some basic information about using Fourier series. This is what I made: ...
3
votes
1answer
91 views

Why is Cos[Abs[x]] Fourier transformed to 0 in mathematica?

I found that FourierTransform[Cos[Abs[x]], x, ξ, FourierParameters -> {1, -1}] gives 0, while ...
1
vote
2answers
91 views

Plotting amplitude spectra of modulated message signal

I'm trying to plot the amplitude spectrum of the modulated message signal, I have managed to plot it by working through the maths, expanding out each trig function, and then drawing onto a graph ...
7
votes
1answer
131 views

How do I make an explicit DFT?

So to gain a better understanding of how Discrete Fourier Transforms are done, I'm trying to program one in Mathematica so I can easily check my answers with the built-in Mathematica code. Based on ...
2
votes
1answer
92 views

How to remove the frequency noises in a Fourier Transformation on an experimental data?

This question is a follow-up to a previous question. I need to perform a Fourier Transformation on an experimental data in time-domain, as shown in Fig 1. With the kind help from Daniel Lichtblau ...
2
votes
1answer
64 views

Need help for Discrete Fourier Transform on an experimental data

I have an experimental data, which is basically a time-domain triangle function. Part I: In theory The time-domain figure is shown in Fig. 1(a), and the corresponding frequency-domain figure is ...
1
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1answer
79 views

Deriving the Fourier Coefficients Formulas with a Manual Procedure

I already know that there are built-in functions to compute the Fourier coefficients but I want to derive their formulas manually. In fact, I want to obtain the final well-known formulas for the ...
1
vote
2answers
127 views

How to realize a Fourier Transform on a non-uniform sampling data

I have a non-uniform sampling data (in time domain) from a Michelson interference experiment, as shown in Fig 1. But it was not evenly sampled (the step length was not uniform), because of the ...
1
vote
1answer
74 views
0
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1answer
48 views

How can I plot an exponential Fourier series? [closed]

Iam triying to plot summatory of the next function: (e^(i*n*t*wo)*Sin[n*Pi/2])/(n*pi) I have no problem plotting a trigonometric fourier serie, so the only ...
3
votes
1answer
105 views

Getting correct amplitudes with Periodogram

I'm having some trouble with the function Periodogram, mainly with getting it to produce correct amplitudes for the spectrum it returns. My question is how to fix ...
1
vote
0answers
82 views

Is oscillation seen in data signal or noise? [closed]

I have some experimental data which is well-fitted by 40 terms of a Fourier series. I want to know if the oscillation exhibited is signal or noise. I evaluated the code shown below to plot my data in ...
0
votes
0answers
67 views

Engineering spectral densities using filtered white noise

My goal is to create time-spectrum noise signals with spectral densities $S_{xx}(f)$ for pretty much arbitrary spectral densities (think white noise, lorentzian, $1/f$). In finding advice on how to do ...
12
votes
2answers
12k views

Plotting the frequency spectrum of a data series using Fourier

testData = Table[N@Sin[500 x], {x, 0, 100}]; ListLinePlot[Abs[Fourier[testData]], PlotRange -> Full] Gives me Which I do not expect because the Fourier ...
1
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0answers
66 views

Constructing the spectral density of white noise

My goal is to find the spectral density $S_{XX}(f)$ from a time domain noise signal $X(t)$. The approach should work for general time series, but to illustrate what I've been doing I'll keep it simple:...
0
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1answer
63 views

InverseFourierTransform very slow

I determined a distribution dist = SmoothKernelDistribution[ListOfValues];. Then I determined the FT of the PDF, which is the ...
13
votes
1answer
1k views

Problem with Fourier coefficients

I have just started using Mathematica with v9.0. I am trying to follow a computation from a book on Fourier series with the function $f(x)=x$ on the interval $-\pi < x < \pi$. Here is the code ...
2
votes
3answers
266 views

Using BandpassFilter

https://drive.google.com/file/d/0B7G3oUuZG1TwRHNNV1RFZjFWUXM/view?usp=sharing Above I have linked a data set containing a 2 seconds EEG sample I have recorded of someone "blinking". This data set was ...
4
votes
1answer
152 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 function:...
1
vote
0answers
178 views

Inverse Fourier transform not evaluating [closed]

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 ...
0
votes
0answers
61 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
107 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
77 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
144 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
63 views
3
votes
2answers
128 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 ...
4
votes
1answer
151 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
72 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
68 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. ...