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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27
votes
4answers
963 views

How fast is my fidget spinner spinning? A sound experiment!

I would like to measure how fast my 6-bladed fidget spinner spins. To do so, after giving it a hard spin, I gently touch the spinner with a wooden stirring stick to create a buzzing sound which ...
0
votes
1answer
568 views

Fourier Transform plot of a piecewise function

I'm working with financial data. I used "Find Formula" to find an approximate function and then I applied FourierTransform to it. Here are the function and the Fourier Transform: ...
0
votes
0answers
213 views

How to realize the contribution of each row in the Fourier Transform of an image?

Let me first show you what I have done so far. ...
0
votes
1answer
104 views

Fourier transform of $1/\sin(\pi x)$ - a quest to find the sign function!

While performing the following (presumably) correct manipulations in Mathematica, I obtain a result that is missing a sign function. Is there a mistake in my code, or is there some bug in Mathematica? ...
0
votes
1answer
54 views

Integrating problem using interface

lately I tried to develop an interface that will plot the furier sum of a given function up to a given number of terms. The code is here: ...
7
votes
4answers
2k views

Circular Aperture Diffraction Pattern

I am unsure if this is even possible in Mathematica, but my optics professor assigned a project to me on circular apertures and Fourier transforms. I have found plenty on the Airy function, but I am ...
0
votes
1answer
223 views

Ideal/Brick wall Low/High-pass filters: Fourier approach not working

I am trying to take a signal (as a list) and separate it into the low frequency and high frequency parts around some split frequency f. Given that what little signal processing I ever studied is now ...
1
vote
1answer
293 views

2D Fourier transform of annulus

I have an annulus and I'd like to the take the 2D Fourier transform of it, my code: ...
0
votes
1answer
512 views

FFT of data to obtain resonance frequencies and correct amplitudes

I have often to do with experimental data (with a certain length and given sampling frequency) where I obtain trajetories of moving objects in 2d. Then I am interested to find out what the ...
1
vote
3answers
95 views

TrigReduce applied to certain terms? Finding coefficients of trig terms

I have an expression that involves trig functions of t and y. I would like to find the coefficients of ...
0
votes
0answers
60 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 ...
5
votes
1answer
141 views

FourierParameters causing function not to simplify

When evaluating this expression, Mathematica simplifies the result: FourierTransform[FourierTransform[u[t], t, s], s, t] This simplifies to ...
0
votes
1answer
93 views

Minimum Sampling Frequency for a 20-term expression [closed]

How can I determined what the minimum sampling frequency should be for the 20-term expression for the function ...
0
votes
2answers
1k views

How do I plot the Fourier series for a square wave? [closed]

f (t) = (4/pi) Sum[(1/n) sin (2 pi (f (t))), {n, 1, Infinity}]
7
votes
1answer
668 views

Discrepancy between Matlab and Mathematica Fourier parameters [duplicate]

MATLAB and Mathematica have different FFT normalization parameters. This is easy to change in Mathematica with the FourierParameters -> argument, but anything ...
1
vote
1answer
86 views

Weird plot for the discrete Fourier transform of a normal distribution compared to Matlab

In mathematica, why does Print[ListPlot[Fourier[RandomReal[NormalDistribution[], {100000}]],PlotRange -> All]]; return an empty plot, sometimes with a random ...
0
votes
0answers
436 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 $...
1
vote
1answer
822 views

Detecting beat frequency using FFT

I wrote Mathematica FFT code that works for non-beat signals, eg. Sin[2*Pi/20*x] and more complicated but I can't obtain beat frequency of Sin[2*Pi*(10)*x] + Sin[2*Pi*(11)*x]. Also, what is general ...
0
votes
1answer
124 views

Power spectrum of ramped sine wave, does not converge

I'm trying to find the power spectrum of a linearly-ramped sine wave - i.e. one whose frequency is periodically and linearly ramped with time. I feel like this should be a somewhat easy numeric ...
1
vote
2answers
149 views

NFourierTransform gives wrong result

This is my code: ...
2
votes
1answer
92 views

Using ''Module' and 'Table' to Plot 'Fourier'

I'm trying to make a function that outputs a plot given a particular parameter, whilst using the Mathematica functions Module, Fourier, and Table. This is what I've come up with thus far. ...
2
votes
1answer
651 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 ...
4
votes
1answer
144 views

Apparently incorrect Fourier Series

While trying to compute Fourier Series, i find that It doesn't evaluate both positive and negative parts and hence apparently giving wrong answer. Below is the code that i tried: ...
1
vote
2answers
176 views

PDE in Fourier space

I have a coupled PDE. How can I convert the equation from $(x,t)$ to $(p,t)$, the Fourier space in MATHEMATICA? \begin{equation} \frac{\partial c}{\partial t} +\frac{\partial d}{\partial t} = -4\...
2
votes
1answer
324 views

Fourier transform along only one dimension of 2D array

I'm a relative newbie to Mathematica Before you flag me as duplicate, note that I have read and studied "Fourier transform over a custom dimension" as best I can. I cannot understand the answer, it ...
2
votes
1answer
110 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 ...
1
vote
2answers
77 views

Integral Transform of exponential function over the positive axes

How do you integrate $\int\limits_0^{\infty} e^{i \omega x}\ \mathrm dx$?
6
votes
1answer
535 views

Implement finite Fourier transforms

Recently I came across finite Fourier transforms, which can be used for solving certain type of boundary value problem (BVP) of linear partial differential equation (PDE) with constant coefficient. ...
1
vote
0answers
102 views

wavelet fourier transform

I want to do wavelet Fourier transform of my data but I have few doubts in this. 1)first of all what is octive and voice command here when i am changing value according to that my plot is changing but ...
2
votes
1answer
584 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
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 ...
1
vote
1answer
59 views
0
votes
1answer
78 views

A problem occurs when extracting specific positions of a discrete Fourier transform [closed]

By the definition in Wolfram language, an expression Fourier[list,{p1,p2...}] will return specific positions (p1,p2...) of the discrete Fourier transform. It dos ...
0
votes
1answer
731 views

How to deal with highly oscillatory integrand when using “NIntegrate” and have a precise result

FTw][n_][w_]:=NIntegrate[ax[n][1][t]/.sol2]Exp[i w1 t],{t,0,600}] Plot[Abs[FTw[1][w1]],{w,1,3}] Here I'd like to calculate the Fourier transform of a complicated ...
2
votes
0answers
165 views

Analysis of the periodic data by the maximum entropy method

I am trying to get the frequency spectrum of periodic data. Since the data set is short, the outcome of the frequency peaks are not sharp enough for me to do further analysis. I know the spectrum can ...
0
votes
1answer
628 views

Generating a sawtooth wave [closed]

I would like to build this piecewise function Please help me to find the appropriated code. P.S: In a second step, I would like to obtain the Fourier series of this function.
0
votes
1answer
242 views

Explicit Discrete Fourier Transform to Kronecker Delta?

How can I have mathematica automatically simplify expressions like this Sum[Exp[-I x k], {x, -Infinity, Infinity}] using ...
0
votes
1answer
209 views

Discrete fourier transform vs analytical fourier transform [duplicate]

I have a function (myfun): scale = 3; fun[x_] := E^(-(x^2/2))/\[Pi]^(1/4) myfun[x_] := fun[x/scale]/Sqrt[scale] that is normalized: ...
5
votes
5answers
648 views

How can I get a discrete result from NDSolve?

When I use NDsolve to solve a differential equations, it returns an interpolation function of the discrete result. Because I haven't found another way to do Fourier ...
4
votes
1answer
216 views

Asymptotic behavior of Fourier transform of $\exp(-x^4)$ at large $k$

I am computing the Fourier transform $$\int_{-\infty}^{+\infty}\mathrm{d}x\,e^{-x^4+ikx}$$ for large $k$. Since $e^{-x^4}$ is $C^{\infty}$ on the whole real line, I expect its Fourier transform to ...
0
votes
0answers
75 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 ...
10
votes
2answers
574 views

A more convenient Fourier series

Personally, I feel the design of FourierSeries/FourierSinSeries/FourierCosSeries/...
0
votes
1answer
114 views

Compute fourier transform of huge list of functions faster [closed]

I want to compute the Fourier transform in the form of trigonometric functions from a list of functions. Suppose I have F1 like below: ...
1
vote
0answers
195 views

Comparison of Discrete Cosine Transform and Discrete Wavelet Transform

I would like to compare the sorted coefficients of the Discrete Cosine Transform with that of the Discrete Wavelet Transform using the Haar wavelets. From theory, the discrete wavelet transform offers ...
0
votes
0answers
96 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 ...
3
votes
2answers
159 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 ...
0
votes
1answer
153 views

Numerical Integration With Many Singularities

Is possible a solution to this Numerical Integration? The constant values are as follows: ...
-5
votes
1answer
150 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; ...
0
votes
1answer
134 views

Numerical Fourier transform of an infinite-order polynomial

I was looking to numerically compute the Fourier transform of a function which can formally be represented as the infinite-order polynomial $$\varphi \, (\zeta ) = \sum_{t=0,2,4,\ldots}^\infty (-1)^t\,...
0
votes
1answer
162 views

How do I get the period/amplitude/sine function from a Fourier transform? [duplicate]

If I have my list peaks from a Fourier transform of a list of values, how can I find the period / amplitude / function approximation of that original list of values from those peaks? I have seen ...