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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FourierTransform is really inverse Fourier transform? [duplicate]

New Mathematica user here. I was trying to use FourierTransform today and getting perplexing minus signs in places I didn't expect them. After perusing the ...
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1answer
170 views

Inverse Fourier transformation discrepancy between Wolfram|Alpha's solution and mine [closed]

I searched for the inverse fourier transformation of $$ \mathcal{F(\omega)} = \frac{2}{(1+i\cdot \omega)^2 +4} \rightarrow i^2=-1 $$ My solution (compliant with the solution from my textbook): $$ \...
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1answer
3k 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,...
3
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1answer
122 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 ...
3
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1answer
4k views

Fourier Series of “Split” Defined Function

Not sure how to phrase this in a concise way, anyway it seems like the function FourierSeries assumes the interval for which to compute the Fourier coefficients of a given function is $[-\pi,\pi]$, ...
3
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1answer
247 views

Fourier transformation of image in only 1 dimension

I have the following image: img = Import["https://i.imgur.com/Peu6mwd.png"] Each column shows the y coordinate of some objects (each row is 0.012 mm apart) and the ...
3
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1answer
473 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 addition, ...
3
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1answer
245 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 $...
3
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1answer
50 views

How does the Fourier transform take its input?

I'm using the Fourier command and I'm wondering how does it take its imput. I know that it takes a list of numbers representing a function of time and it gives back a list of numbers representing a ...
3
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2answers
207 views

Fourier transform of a bivariate normal distribution

I can define a Multinormal distribution by p = PDF[MultinormalDistribution[ {mu1, mu2}, {{sig11^2, ρ sig11 sig22}, {ρ sig11 sig22, sig22^2}}], {x, y}] I would ...
3
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1answer
830 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
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1answer
293 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
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1answer
378 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
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1answer
323 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
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1answer
113 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
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1answer
506 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
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1answer
169 views

Fourier transform of Log[RealAbs[x]]^2

At least one of the outputs (highly likely both) ...
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0answers
57 views

Numerical evaluation of convolution: one more question

Recently I have asked the question about convolution and how to calculate it numerically. I still misunderstand the following moment: if I have two functions defined on a grid ...
3
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0answers
57 views

Structure factor of fourier transform of an image

In this article authors show crystal and liquid phase from two dimensional crystals by calculating structure factor (Fourier transform of 2D points). I have generated set of points in 2D that ...
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0answers
290 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,...
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97 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 ...
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0answers
435 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 ...
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0answers
217 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 ...
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0answers
428 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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0answers
580 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)...
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0answers
215 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 ...
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3answers
499 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.
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2answers
155 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
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3answers
563 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
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2answers
655 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
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1answer
931 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
105 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....
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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
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1answer
926 views

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

I have a matrix that looks like this ...
2
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1answer
106 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
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1answer
98 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
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1answer
643 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
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1answer
310 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
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2answers
1k 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
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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
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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
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1answer
80 views

Amplitude and Phase of a Periodic Signal (Fourier Series) [closed]

Please consider the following periodic signal (by "w" I mean Omega naught): f(t)= Cos(wt)+3sin(2wt)+5cos(6wt) How to plot its amplitude and phase spectrum exactly like the format and pattern ...
2
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1answer
62 views

Numerically Inverting Characteristic Function with Inverse Fourier Transform

I'm trying to numerically invert this characteristic function: ...
2
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1answer
85 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
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1answer
882 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
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1answer
122 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
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1answer
874 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
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1answer
58 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
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1answer
154 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)) ...

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