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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1answer
75 views

Integration not working

Can't seem to get this integration to work. s, n, b, b, l are all constants. ...
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0answers
45 views

Trouble with computing a Fourier transform

I am able to compute the Fourier transform of the general form Exp[-Sqrt[t]] as shown here: ...
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0answers
63 views

Discrete convolution power

In my previous question we have discussed the posibility of various definition of convolution of power function within Mathematica. Now the question is "How to define convolution power in Mathematica ?...
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0answers
52 views

Why does FourierSinSeries return zero? [closed]

I wonder why FourierSinSeries returns 0 in this case: ...
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2answers
208 views

Strange result of FourierCosCoefficient on $\cos^2 t$

The following strange answers were just reported in Mathematics.SE. The OP was asking about the Fourier cosine series of the function $$\cos^2t=\frac12(1+\cos 2t).$$ That question is about WA, but ...
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0answers
39 views

Fourier on chosen dimensions

I have a data set DATA in 4 dimensions $A \times B \times C \times D$ and I want to use the Fourier function net only on the 2 ...
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0answers
40 views

Evaluating Fourier coefficients when Exponential terms are present

I am trying an analytical solution for a 3D Laplace equaition, and just wanted to know if I could use the symbolic calculation capabilities of Mathematica to calculate the Fourier coefficients ...
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2answers
321 views

Fourier series of an arbitrary periodic piecewise function

Let's take a switch function as an example: $ u(t)= \begin{cases} 1, & \text{$0<t<dT_s$} \\ 0, & \text{$dT_s<t<T_s$} \end{cases} $ How can I get Fourier series of it in ...
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1answer
227 views

Which FFT algorithm does `Fourier[…]` use?

Does anyone know which Fast Fourier Transform algorithm Mathematica uses to compute a Discrete Fourier Transform using Fourier[...], and is there any option to ...
4
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1answer
148 views

Why does Fourier give me a different picture than ImagePeriodogram?

I want to take a 2D fourier transform of some data, but when I try this I get unexpected results. When I use ImagePeriodogram I get something that looks like I ...
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2answers
239 views

Fourier Transform to help guess with NonLinearModelFit

I imported some data in Mathematica which I cleaned a bit. This process went well. I also managed to plot it, and tried to take the Fourier transform of the data and plot it again. I'm not sure if I ...
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0answers
59 views

Fourier parametric plot running into “Iteration limit of 4096 exceeded.”

I am trying to create a fourier drawing tool like this but am running into an iteration limit on larger images. Being quite new to mathematica, how could I go about fixing this / making the program ...
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1answer
84 views

DFT and continuous Fourier transform gives different result? [closed]

I am working on the inverse Fourier transform of $\frac{\sqrt{|k|}}{i(|k|-\omega)-\Gamma}$ with $\omega=100, \Gamma=1$. For continuous Fourier transform, I get the following result: ...
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1answer
112 views

applying a fourier sin series fit and then doing a fourier transform

I tried to fit a fourier sin series onto this data with the two different following codes. ...
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2answers
105 views

Polynomial fit and Fourier transform plot

I'm pretty new to Mathematica so excuse me for obvious questions. I have a dataset, second column contains invoice amount and the first column contains days passed between each invoice date starting ...
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1answer
86 views

Plot beat waves spectrum

I have a signal composed of 3 waves oscillating at a high frequency (~10^15 Hz) separated in frequency by 10MHz. I want to simulate the resulting beat wave spectrum. I am expecting a two-peak spectrum,...
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2answers
97 views

How do I find the n-th Fourier coefficient of a function?

I have to define the function f: π for x ∈ (-1,1) 0 for all the others. How do I find the n-th coefficient of this function in the Fourier series expansion for (-...
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3answers
209 views

Another way to calculate frequency from Fourier transform

I have some trouble with calculating frequency after Fourier transform. My code: ...
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1answer
67 views

Mathematica stuck at running symbolic multidimensional Fourier Transform

I'm trying to compute the analytical FT of a bidimensional exponential decay as follows: $f_E(\vec{x}) = \exp \left( - \sqrt{ (\vec{x} - \vec{\mu})^T \Sigma^{-1} (\vec{x} - \vec{\mu}) } \right)$ ...
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1answer
51 views

FourierTransform and Integrate don't agree [closed]

With the input f[t_] := Cos[2 Pi t] FourierTransform[f[t], t, w, FourierParameters -> {0, -2*Pi}] I get ...
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0answers
70 views

Is there a way to find the Region of Convergence along with the Laplace Transform?

This is what I've tried so far. Is the inequality of the conditional expression the Region of Convergence? Why doesn't LaplaceTransform Generate conditions here? ...
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1answer
137 views

How to get exact frequencies in the time response using InverseFourier?

I have amplitude data varying with frequency for a signal. From that I want to generate time response in such a way so that if I take Fourier I can get the ...
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0answers
228 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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0answers
122 views

Fourier transform of non-uniform sampled data

I need to perform an inverse Fourier transform of this set of data, which is in the frequency domain (the x-axis is in $\mu$Hz). However, I'm having two doubts $-$ firstly, this spectral spacing is ...
2
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1answer
403 views

Generate noise time series with given data's PSD

I have PSD data as a 1D array, function of frequency(rad/sec). It is like powerspectrum for damped oscillator. Considering 3 modes, PSD is shown here. I want to generate noise time series which ...
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1answer
160 views

Periodogram local maximum

I want to find dominant frequencies of periodogram exactly. ...
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2answers
182 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 ...
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1answer
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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0answers
78 views

Need to find Fourier series of the following graph

Need to find Fourier series of the following graph.....question is also written in figure.
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1answer
106 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'...
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0answers
41 views

How to force the output to be in terms of a specific function?

I have a rectangular function rect[t], which is a window function with values of $ 1 $ in the interval $ (-\frac{1}{2},\frac{1}{2}) $:- ...
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0answers
61 views

For Fourier Transform with $ x(t) $, how to obtain result in terms of $ X(f) $?

I have a function $ x(t) $ and I denoted its Fourier transformation as $ X(f) $. I want to get the Fourier transformation of $ x(t)\mathrm e^{2\mathrm i \pi f_0 t} $, and I know the result is $ X(f-...
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1answer
220 views

Get frequency axis in Fourier transform (and save them)

I am trying to get the Fourier transform of a light-curve (with an even number of points, 300, and equally spaced in time, 6.9 seconds) and my problem is to get the frequency on the x-axis. I can ...
2
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1answer
128 views

Discrete Fourier transformation from ASCII (for noob)

I am not familiar with Mathematica (I am a physicist programming in Fortran) and my knowledge of it is very limited, unfortunately. I would like to perform the Fourier trasform of a lightcurve which ...
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1answer
145 views

is there a way to avoid the Dirac Delta in the fourier transform?

I would like to compute the fourier transform of H1[t], as you can see the output of mathematica gives the the dirac delta: ...
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0answers
64 views

Frequencies for Fourier coefficients [duplicate]

I have been given the task of calculating the frequencies to which the fourier coefficients correspond. So my input is a discrete signal [1,4,0,1], which gives me <...
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1answer
121 views

Spectrogram of low-frequency data

I generate the following data data = Table[Sin[2 π*100*t] + Sin[2 π*140*t], {t, 0, 10, 1/1023}]; and the spectrogram, as expected, shows two horizontal lines ...
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1answer
174 views

How to use fast Fourier transforms (FFT) to calculate derivatives of a function?

Suppose we have a function numerically defined at pseudospectral collocation points ...
3
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1answer
102 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): $$ \...
2
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1answer
168 views

Re and Im relationships without Abs among Fourier, FourierTransform, InverseFourier, and InverseFourierTransform

Is there a way to make Fourier's Re and Im components separately track the results of ...
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3answers
555 views

Find Fourier Series/Coefficients with Mathematica

Hello I want to find the Fourier series and/or the coefficients for a function like the following: or or For the first one I did the following: ...
2
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1answer
119 views

Fourier Transform of a symbolic expression

Hello I would like to do the Fourier Transform of H1'[t - L2[t]/c - L2primo[t]/c] I know that its transform has to be: ...
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1answer
77 views

Plot the graph of the square wave function defined as $f(t)=\sum^{\infty}_{n=0}(-1)^n h_{n}(t)$ on the interval $t>0$ and find its Laplace transform

Plot the graph of the square wave function defined as $$f(t)=\sum^{\infty}_{n=0}(-1)^n h_{n}(t)$$ on the interval $t>0$ and find its Laplace transform. The http://mathworld.wolfram.com/...
3
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1answer
135 views

Indeterminate result from Sinc

I have an impulse train given by (1 + Csc[(π x)/(1 + R)] Sin[(π (1 + 2 R) x)/(1 + R)])/(2 + 2 R) Because of the Csc, ...
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0answers
69 views

Shift a signal in time using Fourier Transform and Inverse Fourier Transform

I am trying to time-shift a signal x, which is a sine wave with 10 sec time-period, by t=2 seconds to get shifted version ...
2
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0answers
81 views

Use List convolve for aligning images

I am trying to align images of point spread functions using a convolution. Before doing it on real data, I wanted to try on simulated data. I have no problem with the 1-D case where I create 2 ...
9
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2answers
308 views

Frequency of ticks in mechanical watches

I'm looking to find the frequency of a relatively large dataset (or a relatively short audio file) of a repeating sound, like so: Here are the original files, for those willing to play. :) eta2412 ...
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1answer
117 views

Implementation of discrete Fourier Transform in Matrix Form

I am trying to gain an in depth understanding of how discrete fourier transforms work, and consequently I am trying to implement the discrete fourier transform myself in the form of a matrix. First ...
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1answer
629 views

Fourier Parameters

I need to use the built-in function Fourier, to get the Fourier transformation of a list of numbers. Unfortunately, I would need to set the second argument of the FourierParameter option to a non-...
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1answer
251 views

Fourier transform of a complicated function

This question is related to "Numerical Fourier transform of a complicated function" from 2012. I have pretty much the same problem: I have a function $f(x)$ which is complicated to evaluate, and want ...