# 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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### Integration not working

Can't seem to get this integration to work. s, n, b, b, l are all constants. ...
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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### 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 ?...
52 views

### Why does FourierSinSeries return zero? [closed]

I wonder why FourierSinSeries returns 0 in this case: ...
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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### 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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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: ...
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. ...
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 ...
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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### 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 (-...
209 views

### Another way to calculate frequency from Fourier transform

I have some trouble with calculating frequency after Fourier transform. My code: ...
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: $f_E(\vec{x}) = \exp \left( - \sqrt{ (\vec{x} - \vec{\mu})^T \Sigma^{-1} (\vec{x} - \vec{\mu}) } \right)$ ...
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 ...
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? ...
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 ...
228 views

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### 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 ...
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: ...
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: ...
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/...
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, ...
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 ...
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 ...
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 ...
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 ...
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 ...