Questions tagged [fourier-analysis]

Questions on the discrete and continuous Fourier analysis functions of Mathematica, as well as the FourierSeries` package.

89 questions with no upvoted or accepted answers
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13
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0answers
495 views

Proving (self) similarity with Mathematica - Reccurrence Plots, Similarity Plots etc

I posted this question in math.se but given the sheer tumultuous number of questions that keep appearing on math.se and also given that I am trying to accomplish this in Mathematica, I thought I'd ...
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178 views

The same analytical expression gets inconsistent FourierTransform results

I have an expression which is just a linear combination of plane waves, and I'd like to calculate FT of it. I know what I will get should be a bunch of delta functions, but it turns out Mathematica ...
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179 views

Comparison of Continuous and discrete Fourier Transform

Consider a continuous signal as follows: ...
5
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163 views

Using NIntegrate and DiscretePlot to visualize pseudodifferential operators

In harmonic analysis, pseudodifferential operators are a way to generalize the notions of derivatives, through the use of Fourier transforms. The basic idea being, Let $u(x)\in\mathcal{S}(\mathbb{R}^...
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412 views

Different FourierParameters in each dimension for discrete Fourier transform

I have a query about the Fourier utility, that does discrete Fourier transforms. I am unable to find any information on whether different FourierParameters can be ...
5
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0answers
313 views

Periodogram for irregularly spaced data

I am trying to replicate some existing work on the length of the cycles in certain economic data. Specificially, I am using the Schularick and Taylor (2012) data set to replicate the periodogram shown ...
5
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165 views

Why does setting $Assumptions make my Fourier transforms slow?

Consider these Fourier transforms ...
4
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0answers
358 views

Constructing the spectral density of white noise

My goal is to find the spectral density $S_{XX}(f)$ from a time domain noise signal $X(t)$. The approach should work for general time series, but to illustrate what I've been doing I'll keep it simple:...
4
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0answers
612 views

Help with Fourier analysis and filtering of an image

I am starting with the following image: For the curious, it is an STM scanned image of graphite. I am hoping to find some kind of periodic structure in the image related to the honeycomb structure of ...
4
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0answers
7k views

Fourier Transform of Absolute Value

If you ask Mathematica to provide the Fourier Transform of a singular functions it is likely to provide an answer that while nearly correct, is technically incorrect and it will do so without a word ...
4
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0answers
264 views

What are good/best practices to take the Fourier transform of an InterpolatingFunction?

I have a function which I have obtained from numerical integration of a differential equation, and I would like to take its Fourier transform. What are good practices for doing this? To make things ...
3
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0answers
191 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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89 views

Laplace transform of rapidly increasing function

Consider the following 3 LaplaceTransform expressions. I believe that the first two are valid (at least for k>0). The third ...
3
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386 views

Computation of a Fresnel Diffraction pattern with Discrete Hankel Transform

In the next link: Computation of Hankel Transform using FFT (Fourier) Rainer implemented a great solution given in the next reference: Manuel Guizar-Sicairos and Julio C. Gutiérrez-Vega, "Computation ...
3
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400 views

Calling CUDA cuFFT

Following ybeltukov's excellent answers (see here and here) about how to access the CUDA library functions and interact with Mathematica through CUDAMemory, I tried to compile the code given in ...
3
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0answers
544 views

How to do Fast Fourier transform (FFT) for singular functions?

I want to do a 3-dimensional FFT on this function $\frac{\cos (x) \cos (y) \cos (z)-\sin (x) \sin (y) \sin (z)}{\left((1.0001+\sin (y)+\cos (z))^2+(0.0001+\cos (x)+\sin (z))^2+(0.0001+\sin (x)+\cos (y)...
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0answers
202 views

Fourier transformation of HeavisideTheta functions

I want to find 2D-Fourier transformation of the function given below f = HeavisideTheta[y1]*HeavisideTheta[y2 - y1] For the purpose, I use built-in function in ...
2
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0answers
44 views

Triple infinite summation of a 3D Fourier series

I'm trying to evaluate the equation below excluding the case when $n_x=n_y=n_z=0$. I know this equation converges everywhere except where x,y, and are all multiples of $2\pi$. I've attempted breaking ...
2
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1answer
120 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 ...
2
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0answers
72 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 ...
2
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0answers
83 views

Fourier Cos coefficient vs Integrate vs common sense

I was trying to find out what the (discrete) Fourier transformation of the following function is $$ f(\nu, u) = \frac{\sinh \nu}{\cosh \nu - \cos u} $$ So at first, I tried to evaluate a fancy MMA ...
2
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0answers
62 views

2d vs 1d FourierTransform

According to the documentation, the multidimensional Fourier transform is defined as $$ \frac{1}{(2\pi)^{n/2}} \int_{-\infty}^\infty \int_{-\infty}^\infty \cdots f(t_1, t_2, \dots, t_n) \mathrm e^{\...
2
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0answers
167 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 ...
2
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0answers
75 views

Determining Periodicity with Fourier?

Note: This question has previously been marked as a duplicate of What do the X and Y axis stand for in the Fourier transform domain?. While the answer will likely have an overlap, so the question ...
2
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0answers
32 views

Verifying a cosine FourierTransform

On page 31 of this standard reference we have the following relation: I wanted to use mathematica to verify this transform numerically for some example values. So I type in: ...
2
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0answers
222 views

Can I use Mathematica for the symbolic verification of cases of a general problem?

I have never used Mathematica before, but I am contemplating using it to solve this problem for a simple case of $f(x) = C, 1<x<2$ and $= 0$. I can easily get $\hat{f}$, the Fourier transform of ...
2
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0answers
157 views

4D Fourier transform of $\theta(t^2 - x^2 - y^2 - z^2)$

Possibly this post of mine is bad style in that I am not a Mathematica user, at least not yet; rather I use the competing Maple. My excuse, if at all acceptable to the present community, is that ...
2
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0answers
101 views

FourierCoefficient performance

I encountered weird performance issue while using FourierCoefficient[]. I narrowed it down to calculating $n$-th coefficient for $\cos(nx)$. ...
2
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0answers
54 views

FourierTransform of a gaussian at -1 and 2

Let ft[w_] := FourierTransform[Exp[-t^2], t, w] Then ft[#] & /@ Range[-2, 3] Evaluates to ...
2
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0answers
135 views

Incorrect output from InverseFourierTransform

Bug introduced in 8.0.4 or earlier and fixed in 9.0.1 or earlier I am trying to compute the inverse Fourier transform of this expression ...
2
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0answers
94 views

Calculating the recursion at the Fourier domain

I would like to calculate the following recursion with mathematica $$f_n(x)=\int_{B}^{A}f_{n-1}(x-\omega)f(\omega)\mbox{d}\omega\quad\quad f_1(w):=f(w)$$ This is simply the convolution of $f$ with ...
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0answers
36 views

InverseFourierTransform takes me forever

I am trying to solve complicated PDEs using FourierTransfrom and InverseFourierTransform on Mathematica 12.0, but the code below does not give me a result. I do not get any error messages but the ...
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0answers
30 views

A newbie question about the use of the FourierSeries functions

Although I have had no previous experience with the Mathematica Fourier Series functions ( or package ), I am writing a tutorial on Fourier Analysis and Transformations in a Mathematica Notebook, ...
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56 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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0answers
98 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 ...
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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
192 views

2D Fourier transform of a diffraction pattern Mathematica vs FourierPainter

We are trying to make sense of the numbers provided by the PC program FourierPainter for a 2D Fourier Transform of a diffraction pattern. We would like to evaluate the ratio of the zeroth harmonic ...
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0answers
155 views

Fourier | Examples | Applications | Frequency Identification: high resolution: what trick is this?

My question is regarding one of the examples in the Documentation Center for the built-in symbol Fourier: Fourier | Examples | Applications | Frequency Identification Fourier is used to find the ...
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104 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 ...
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0answers
199 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 ...
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0answers
167 views

Inverse Fourier Transform of Poisson Characteristic Function?

The follow line is returning without evaluation: InverseFourierTransform[ CharacteristicFunction[PoissonDistribution[1], t], t, w] It is meant to output ...
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0answers
133 views

Fourier Transform(first use)

This is in continuation of the question I asked Wrong evaluation of integral in Mathematica? But I will try to make it self contained. I have a periodic function ...
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0answers
77 views

Wrong behavior of Inverse Fourier Transform of DiracDelta[x]/x

The following fails to compute: InverseFourierTransform[DiracDelta[w]/w, w, x] But if we add a, ...
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0answers
199 views

Multidimensional numerical Fourier transform

I'm trying to numerically compute the Fourier transform of the following bump function: $$\hat{r}(k)=\int r(x)e^{ikx}dx$$, where $r\in C^{\infty}_{0}(\mathbb{R}^{2})$, namely: $$r(x)=\begin{cases}\...
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0answers
81 views

evaluate image disorder from FFT?

I have to find some estimates of the disorder in a hexagonal lattice, that is in microscopic images like this (disorderedhex.png): [ I wrote this to simulate these kind of images: ...
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0answers
134 views

Fourier Transform for Blazed Fork Grating

I built blazed fork grating on Mathematica and the idea of using blazed fork grating instead of normal one is to eliminate the other diffracted order. So the blazed fork grating will let only the 1st ...
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0answers
242 views

Assumptions don't work as expected in FourierTransform

The 2D rectangular function and its Fourier Transform is $$ g_{in}(x,\,y) = rect(\frac{x}{x0}) \, rect(\frac{y}{y0}) \quad \xrightarrow{\mathscr{F}} \quad G_{in}(u,v) = x0 \, y0 \, sinc(\pi u x0) \, ...
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0answers
209 views

Perform a Fourier Transform on a wavelength scan

I have a plot of the power transmitted through a device as a function of wavelength, from 1500 to 1600nm. There is some Fabry-Perot noise, plus I suspect some other regularities. I would like to ...
1
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0answers
116 views

Discrepancy between laplace and fourier transform of gaussian

The function in question is Exp[x^2/2] for x>0 Laplace transform should be the same as the fourier transform since the function is absolutely integrable. Fourier: They are indeed the same ...
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0answers
181 views

Discrete Fourier Transform baseline subtraction

I am trying to remove sinusoidal variability from a set of evenly-spaced intensity vs. time data. These data contain periodic events that are separated by a normalized (but sinusoidally variable) ...