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Questions tagged [fourier-analysis]

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

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3
votes
1answer
638 views

Frequency decomposition of an mp3 file?

After loading an mp3 file test = Import["test.mp3"] I would like to make a plot with x-axis being the frequency of waveforms ...
3
votes
1answer
279 views

Power Spectral Density of the Output Response of a Linear State Space Model

I have the following Linear State Space Model. It is pasted in Normal form for it to be readable. ...
3
votes
1answer
339 views

Fourier Transform accelerogram seismic

I have a seismic accelerogram. I tried to apply the Fourier Transform to interpolate function, but dosn't work. So, i applied the ...
3
votes
1answer
292 views

Why isn't Mathematica outputting the inverse fourier transform of this function?

I'm brand new to Mathmematica, so please be nice. I don't understand where I'm going wrong. I just need to use the method of inverse fourier transform on this wavefunction to get the momentum-space ...
3
votes
1answer
108 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 ...
3
votes
1answer
440 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 $$ \psi(X,Y,z=d)=\underset{aperature}{\iint}\psi(x,y,z=0)e^{-i\frac{k}{d}\left(xX+yY\right)}dxdy\\\psi(x,y,z=0)=...
3
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1answer
4k views

Plot Fourier transform of $\sin (2 t)$

I'm trying to plot the Fourier transform of $\sin (2 t)$. I tried using the FourierTransform Function (I'm expecting a peak at w = 2) but it gives me undefined at <...
3
votes
0answers
193 views

Deconvolution using Fourier transforms

I have a 2D signal in the form of a function $g(x_m,y_m)$ given as $$ \begin{aligned} g(x_m,y_m) = \ & \int^{\infty}_{-\infty} \mathrm{d}x_o \ \mathrm{d}y_o \ \frac{1}{\varepsilon^2} P(x_o - x_m,...
3
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0answers
89 views

Laplace transform of rapidly increasing function

Consider the following 3 LaplaceTransform expressions. I believe that the first two are valid (at least for k>0). The third ...
3
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0answers
388 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 ...
3
votes
0answers
198 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 ...
3
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0answers
400 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 ...
3
votes
0answers
544 views

How to do Fast Fourier transform (FFT) for singular functions?

I want to do a 3-dimensional FFT on this function $\frac{\cos (x) \cos (y) \cos (z)-\sin (x) \sin (y) \sin (z)}{\left((1.0001+\sin (y)+\cos (z))^2+(0.0001+\cos (x)+\sin (z))^2+(0.0001+\sin (x)+\cos (y)...
3
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0answers
202 views

Fourier transformation of HeavisideTheta functions

I want to find 2D-Fourier transformation of the function given below f = HeavisideTheta[y1]*HeavisideTheta[y2 - y1] For the purpose, I use built-in function in ...
2
votes
3answers
421 views

Symbolic Discrete Fourier Transform (DFT), using FFT?

Is there an implementation of a symbolic FFT in Mathematica? I've looked around, but I can't find any; Fourier seems to only give numerical results.
2
votes
1answer
184 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 ...
2
votes
2answers
110 views

Figuring out the frequency components using FFT [duplicate]

The function defined below has three frequencies 2, 4 and 10. How to use the Fourier transform (FFT) to show these frequencies? ...
2
votes
3answers
494 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 ...
2
votes
2answers
596 views

Integration and Fourier transform

I would like to calculate the distribution function from the characteristic function. There is a formula given as $$F_X(x)=\frac{1}{2}+\frac{1}{2\pi}\int_{0}^\infty \frac{e^{i w x}\phi(-w)-e^{-i w x}...
2
votes
1answer
871 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: ...
2
votes
1answer
96 views

Slow execution in Fourier analysis [closed]

The following example executes and plots a Fourier transform of a integrable function. Can anyone suggests why the execution is so slow (about 1 min on a laptop Intel(R) Core(TM) i7-4600U CPU @ 2....
2
votes
3answers
1k 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 ...
2
votes
1answer
768 views

How to use a Fourier Transform to find the frequency spectrum of Eigenvectors?

I have a matrix that looks like this ...
2
votes
1answer
82 views

FourierTransform frequency

In wikipedia's Fourier Transform site there are tables of important FTs, the thing is that Mathematica always considers angular frequency. Is there a way to get what is in the second column labeled ...
2
votes
1answer
92 views

For what range of frequencies is the Fourier function defined?

I am interested in evaluating the discrete Fourier transform for a list of data. The problem is the results given by the function Fourier depends on the length of ...
2
votes
1answer
574 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 ...
2
votes
1answer
303 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? ...
2
votes
2answers
921 views

2D Fourier transform of a table - ArrayPlot issue

Recently, I have encountered an issue with ArrayPlot after performing a Fourier transform of a table. Picture presented above is an ArrayPlot of a 2D table. Using Fourier on this 2D table I obtain ...
2
votes
2answers
3k views

Discrete FFT of non-periodic signal excited by short pulse

Say I have a signal F(t) which represents a excitation by a pulse (so it is not periodic and declining to zero amplitude). According to this answer, for instance, ...
2
votes
1answer
2k views

discrete Fourier transform

I generate a periodic discrete data representing a time dependent function and I want to apply a discrete Fourier transform to this data using just one period of it. I think something is wrong with ...
2
votes
1answer
61 views

How to shift function (like RotateRight) in the y direction?

I'd like to shift my graph so the periodogram is centered. I was able to rotate the original using Rotate Right, but now I can't shift the graph in the y dimension. Thank you for your help! ...
2
votes
2answers
159 views

Fourier Phase Angle Interpretation

I am trying to fit the following tide data (taken from here) with a sinusoidal curve that looks like the following: displacement+amplitude * sin(t w - ph), where t is the independent variable, w is ...
2
votes
1answer
113 views

How to turn the internal sound note into the form of function

I want to make a brief Fourier transformation of the sound notes of the same pitch but played by different instruments to see the difference of their Fourier ...
2
votes
1answer
766 views

Finding peaks on a Periodogram

I am currently working on a school project involving modelling sound recordings of piano notes. I have used the periodogram function to graph my recording and would like to find the peaks of this ...
2
votes
1answer
57 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 ...
2
votes
1answer
151 views

Tough Inverse Fourier Integral: why does the sign matter?

I'm computing the Inverse Fourier Integral of ((a^2 + omega ^2) c^2) /((b^2 + omega^2) ((r^2 + omega^2 - omegaInt^2)^2 + (2 omegaInt r)^2)) ...
2
votes
1answer
103 views

Unexpected behaviour of PowerSpectralDensity

I recently wanted to calculate the power spectral density of a surface profile. I was happy to find out that there is a built in PowerSpectralDensity[] function in Mathematica (version 10). However, I'...
2
votes
1answer
460 views

Problem with Fourier transform

How to define a top hat function with plot also at opening and closing value? and How to plot a Fourier transform of the function?
2
votes
1answer
678 views

Solving the heat equation on the semi-infinite rod

Cross posted in scicomp.SE. I want to test the solution which is given below is right by Mathematica. Please look the post in mathstackexhange or Please look below. Question: Solve the ...
2
votes
1answer
2k views

Using mathematica to take fourier transform of data

I'm trying to use Mathematica to take a discrete Fourier transform of 68 data points (0 to 67) to perform further analysis. My data points, when plotted, look like this: Pretty straightforward. Now,...
2
votes
1answer
97 views

Change FourierParameters in CUDAFourier

CUDAFourier does not have option FourierParameters. I need to change its convention. It has default ...
2
votes
1answer
269 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
135 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 ...
2
votes
1answer
2k views

Integrate message: can't prove Integration limits are real

I'm working on solving differential equations through Fourier series, I made a function to help me calculate the coefficients that looks like this: ...
2
votes
1answer
957 views

How to manipulate a Fourier sine series?

I would like to plot the Fourier sine series for $f(x) = x$. I would like to manipulate the parameter n from $0$ to $10$ and plot the sine waves over $(0,1)$. My ...
2
votes
1answer
2k views

Fourier transform of sampled data

I have got some impulse response data that I would like to transform via Fourier to get the amplitude-frequency characteristics of the performing loudspeaker. The ...
2
votes
1answer
32 views

How to Mathematica applied discrete Fourier transform to matrix?

I am new user of Mathematica, sorry if my question odd. I not understanding, how to Mathematica apply the discrete Fourier transform for matrix: ...
2
votes
1answer
603 views

Cut off frequency of low pass filter

I have a data here, I want to make sense of Lowpass filtering function in Mathematica.I do not fully understand units of cut off frequency in this option since the data is in frequency space. What I ...
2
votes
1answer
186 views

Fourier transform question

Consider the fourier transform FourierTransform[1/((Cosh[x] + 1) (Cosh[x]^2 - 1)^(1/2)), x, w] If I execute the above line, Mathematica thinks for several ...
2
votes
1answer
371 views

How to perform this numerical Fourier transform?

For $t\in\mathbb{R}_{\ge 0}$ and $s\in\mathbb{R}$, let $$f(t)=\begin{cases}\int_{0}^{t}\exp\left(-\frac{1}{1-s^{2}}\right)\,ds,&|s|<1, \\ 0,&|s|\ge 1\end{cases}$$ I plotted this without ...