# 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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### Why does this Fourier transform not match the formula?

From this page: So I'm trying to get that result in Mathematica. From the fourier formula above, we can see that {a, b} = {1,-1}. However, the code below returns a different result. ...
1 vote
81 views

### Can I take the Fourier transform of a PDE in both sides? [duplicate]

I want to know if it is possible to use a PDE in the function FourierTransform instead of a function. Consider for example the simple case for the heat equation ...
1 vote
101 views

### Nonlinear Schrödinger Equation With Periodically Varying Function

I am trying to solve Equation. 42 from https://labsites.rochester.edu/agrawal/wp-content/uploads/2019/08/paper_2019_03.pdf The equation I am trying to solve is a nonlinear Schrödinger equation More ...
204 views

### Collision of two waves with phase difference

I am trying to produce collisional figures from this paper https://arxiv.org/pdf/1803.07165.pdf. But failed to see the phase effect. In my case it just passes through one another. It basically solve a ...
1 vote
61 views

### Inverse Fourier Transform and the sign of the Shifted Delta

I am using the sign convention of FourierParameters->{0, -2 Pi} for calculating the inverse FT of $Aexp(-2\iota\pi f K)$, where $A$, $K$ are real numbers >0 ...
169 views

### I am trying to solve nonlinear Schrödinger equation with dipolar interaction

I am trying to solve numerically Equation number (29) with the help of Eq.(32) and (34) from this paper https://arxiv.org/pdf/1506.03283.pdf. for ...
39 views

### Convolution theorem if one function depends on the reciprocal space in a non-trivial way

I would like to write the following integral in terms of a convolution: \begin{equation} H(x_1,x_2) = \int dt e^{\mathrm{i} t (x_1+x_2)/2} f(t,x_1,x_2) g(t), \end{equation} where $f(t,x_1,x_2)$ ...
1 vote
51 views

### Implementing the Shift Property of the Fourier Transform in Mathematica

I am trying to determine the Fourier tranform of a time shifted (t-b) Lorentzian function in Mathematica. With the zero centered Lorentzian (b=0), the Integrate function with the conditions that all ...
81 views

### Obtaining Inverse Fourier Transforms by "FourierTransform" vs. "Integrate" Option [duplicate]

I am trying to calculate the inverse Fourier transform of "1" using two approaches. One using the Integrate option and the other with InverseFourierTransform, so the function looks like the ...
72 views

### How to use FindSequenceFunction to obtain the general expression of Fourier series?

I want to get cosine series of the following functions. $f(x)=\left\{\begin{array}{cc}\cos x, & 0 \leqslant x<\frac{\pi}{2} \\ 0, & \frac{\pi}{2} \leqslant x \leqslant \pi\end{array}\right.$...
1 vote
42 views

### Why does the following integral not evaluate? [closed]

I am a complete beginner to Mathematica. I am trying to evaluate a Fourier integral (see below). Here $\mu(\vec{r})$ is a mass density with units $[\frac{u}{mm^3}]$, and its Fourier transform is ...
53 views

### Why would the computation time be hugely different for the same computation expressed in different but totally equivalent forms?

I was trying to plot an interpolation function from fourier data. The plot was very fast and straightforward when I used the following code: ...
1 vote
561 views

### Mathematica fourier get different result with python np.fft [closed]

In python,I run fft as below: ...
97 views

### Integrate does not converge while Fourier transform does

Let us say I want Mathematica to compute the integral $$\int dx \, \text{sign} (x) \, \frac{1}{1+x^2} = 0 \, .$$ Indeed ...
71 views

1 vote
78 views

### Is there a function in Mathematica to combine/decompose sinusoids? [closed]

Lets say I have some combination of an arbitrary number of sinusoids with potentially varying magnitudes, phase angles and frequencies that I would like to compose into a singular sinusoid, is there a ...
92 views

### Microfluctuations analysis and Power spectrum

I measured a parameter over time and obtained the values below: 0,627896 0,205004 0,259237 1,059125 0,832184 0,587992 0,565537 0,527323 0,460228 0,471958 0,26696 0,75367 ...
79 views

### 2D Poisson equation with Piecewise RHS - symbolic solution?

I'm trying to solve the following 2D Poisson equation symbolically:  -\nabla^2 u(x,y) = \begin{cases} 1-\text{sech}\left(\frac{w}{2 d}\right) \cosh \left(\frac{x}{d}\right) & -w/2 \leq ...
51 views

### Debugging code with Plot function. Full details

This is some code: The first plot (with the f[x,3]) gives me a graph. The second plot (with the 'numerical' form of f[x,3] given) does give me a plot How can I fix this so that the first line gives me ...
467 views

### Useless result of Integrate

Considering a Fourier sine series, I calculate int = Integrate[Log[1 + Sin[x]]*Sin[i*x], {x, 0, Pi}, Assumptions -> i ∈ PositiveIntegers] ...
81 views

### Raising awareness about a Fourier analysis issue [closed]

I have just posted a query on Wolfram's own forum: https://community.wolfram.com/groups/-/m/t/2299913?p_p_auth=HBTdYN1c This is because it allows me to share the notebook I am working on and therefore ...
96 views

### Issues to compute and plot a function with some Fourier analysis

I'm currently in an internship and I have to construct a model that involve Fourier transform of 2 orbitals. My issue is that when I run the programm, the function evluateton non numerical values : &...
1 vote
145 views

### Find FT and r.m.s noise of a signal

I have a signal : ...
108 views

### How to obtain a normalized fourier transform?

In my code I solved a differential equation system, then I made a fourier transform of the solution in differents times, this is my code ...
331 views

### Challenge: Computing the Fourier Series of a List Plot!

I have a bunch of data points (copied from Mathematica below), which I have 'ListPlotted' I would now like to compute the Fourier series of this function (after doing a Fourier transform I assume? Or ...
1 vote