# 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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### 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 ...
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 ...
179 views

### Comparison of Continuous and discrete Fourier Transform

Consider a continuous signal as follows: ...
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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 $u(x)\in\mathcal{S}(\mathbb{R}^... 0answers 412 views ### Different FourierParameters in each dimension for discrete Fourier transform I have a query about the Fourier utility, that does discrete Fourier transforms. I am unable to find any information on whether different FourierParameters can be ... 0answers 313 views ### Periodogram for irregularly spaced data I am trying to replicate some existing work on the length of the cycles in certain economic data. Specificially, I am using the Schularick and Taylor (2012) data set to replicate the periodogram shown ... 0answers 165 views ### Why does setting$Assumptions make my Fourier transforms slow?

Consider these Fourier transforms ...
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### 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:...
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 ...
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### 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 ...
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 ...
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### 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 ...
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### 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 ...
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: ...
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 ...
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 ...
101 views

### FourierCoefficient performance

I encountered weird performance issue while using FourierCoefficient[]. I narrowed it down to calculating $n$-th coefficient for $\cos(nx)$. ...
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### FourierTransform of a gaussian at -1 and 2

Let ft[w_] := FourierTransform[Exp[-t^2], t, w] Then ft[#] & /@ Range[-2, 3] Evaluates to ...
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### 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 ...
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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### 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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### 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, ...
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 ...
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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### 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 $(-\frac{1}{2},\frac{1}{2})$:- ...
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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### 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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### 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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### 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 ...
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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### 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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### 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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### 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 ...