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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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63 views

Prevent running out of memory when doing SpectrogramArray?

I was using SpectrogramArray[Import@"myFile", 22050, 22050]to transfrom a piano mp3 file so that I can (probably?) generate a midi file from that mp3. The step size ...
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479 views

Fitting by Fourier series and their coefficient [duplicate]

I have two arrays contain $y$ and $k$,respectively. However, the exact function relationship is not clear. What I what to do is to fit $y(k)$ by Fourier series $\qquad y=\sum_n c_n \cos(nk)$ up to $...
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77 views

Numerical error or mistake when filtering using Fourier?

I am comparing the filtering method using a recurrence filter with filtering using Fourier. I think both methods should give the same answer but they differ by a small amount that could be numerical ...
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109 views

Multidimensional DFT of function

Assume that we have a well-defined real-valued functionf[x,y,z] whose (inverse) Fourier transform is impossible to solve for symbolically and numerically using ...
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98 views

Help with Frequency Identification with Fourier? [duplicate]

Note: This question has been marked as a duplicate of What do the X and Y axis stand for in the Fourier transform domain?. While the answer will likely have an overlap, so the question should be ...
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67 views

(Naive) Manual implementation of DFT results in long sum which is very inefficient to plot, can my approach be saved?

I will do my best to keep this question as short as possible, I am afraid though that I wont be able to get my issue across if I don't elaborate on the background and provide my code as an example. ...
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85 views

Identify frequency components

I try to perform data analysis on wind power production. Data consist in 17520 points, corresponding to the production averaged over 30 minutes over the 365 days of the year. I somehow expect to see ...
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81 views

Problems with sampling

Let $t\ge 0$ and let $f_{s}(t)$ be the sampled version of $f(t)$. If $$f(t)=\begin{cases}\int_{0}^{t}\exp\left(-\frac{1}{1-s^{2}}\right)\,ds,&|s|<1, \\ 0,&\text{otherwise}.\end{cases}$$ I ...
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93 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 ...
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319 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 ...
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84 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 ...
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36 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: ...
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30 views

Result from FourierCosCoefficents does not appear to be linear [closed]

f3 and f4 below produce the same output (more or less) but the coefficient in f3 does not appear to be the sum of f2 and f1 (which it should, uiam).' ...
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1answer
123 views

Unable to get the correct Dirac delta Fourier transform [closed]

I wrote ω = 2 πf; τ = 1/f; FourierTransform[β*Cos[ωt], t, ω] I expected constant x DiracDelta(-omega1+omega)+constant x DiracDelta(omega1+omega) the answer ...
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436 views

A piecewise function with way too many pieces

I'm currently calculating a periodic square wave current function to feed into a particle accelerator. It's a square wave that ramps up to a certain frequency and then drops back to the base frequency ...
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1answer
157 views

Heat Equation 3-D

I'm new to using Mathematica software, and I need to solve a problem involving the Heat Equation for a quadrangular (3D) prism. I have the equations below and I need the temperature x time graphs; ...