# 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. ...
• 1,750
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 ...
• 115
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 ...
• 121
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: $$H(x_1,x_2) = \int dt e^{\mathrm{i} t (x_1+x_2)/2} f(t,x_1,x_2) g(t),$$ where $f(t,x_1,x_2)$ ...
• 818
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 ...
• 121
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 ...
• 121
72 views

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

I want to get cosine series of the following functions. $f(x)=\left\{\begin{array}{cc}\cos x, & 0 \leqslant x<\frac{\pi}{2} \\ 0, & \frac{\pi}{2} \leqslant x \leqslant \pi\end{array}\right.$...
• 1,365
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 ...
• 129
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: ...
• 43
1 vote
561 views

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

In python,I run fft as below: ...
• 697
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 ...
• 257
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 ...
• 51
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 ...
• 3,870
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 ...
• 203
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] ...
• 16.6k
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 ...
• 103
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 : ...
• 157
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 ...
• 103
1 vote