The Stack Overflow podcast is back! Listen to an interview with our new CEO.

Questions tagged [fourier-analysis]

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

455 questions
Filter by
Sorted by
Tagged with
510 views

Fourier Transform of Square Functions [closed]

I wanted to visualise at how the frequency spectrum of square waves changes with duty. But I got stuck at the first hurdle: FourierTransform[SquareWave[x], x, w] ...
53 views

What is the correct way to represent this sum?

The summation of Fourier series of Sin[x-x[i]] at three location x to x is: ...
66 views

NIntegrate option for FourierSeries

I would like to use FourierSeries but it is very slow. My guess is that it is because it uses symbolic integration: ...
197 views

Finding periodicity of multidimensional data?

I have a data set consisting of measurements of an $n$-dimensional vector $\mathbf{x}(t)$, at $N$ distinct time points $t_i$. The time points $t_i$ are equally spaced. I need to find the dominant ...
274 views

Generate noise time series with given data's PSD

I have PSD data as a 1D array, function of frequency(rad/sec). It is like powerspectrum for damped oscillator. Considering 3 modes, PSD is shown here. I want to generate noise time series which ...
138 views

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 ...
333 views

Fourier transform along only one dimension of 2D array

I'm a relative newbie to Mathematica Before you flag me as duplicate, note that I have read and studied "Fourier transform over a custom dimension" as best I can. I cannot understand the answer, it ...
184 views

Implement inverse discrete-time Fourier transform

In Mathematica after version 9. We had ListFourierSequenceTransform to do discrete-time Fourier Transform, but we do not have the inverse function. If we peform it ...
517 views

105 views

Fourier transform of imaginary exponential with absolute value argument [closed]

When asked to compute FourierTransform[Exp[(-I*Abs[x])], x, k, FourierParameters -> {1, 1}] Mathematica returns ...
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 ...
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 ...
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 ...
68 views

Finding covariation between datasets [closed]

For me this is a very fascinating problem, which I however lack the ability to deal with as well as the nomenclature to describe properly. (Please feel free to edit the title). The conditions are the ...
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 $\cos(nx)$. ...
124 views

How to do the Fourier transform of a picture? [duplicate]

I want to generate Fourier transforms of a picture. the transform can represent the diffraction pattern of the picture. Basically, if I have a picture. Then, the result should look like this: For a ...
247 views

How can I analyse and manipulate k-space data of a DICOM imageset? [closed]

I'm very new to Mathematica. I've some MRI images as 3D DICOM data. I want to get the corresponding k-space data to identify all the signals with their corresponding amplitude, frequency and phase. ...
67 views

How do I let Fourier Transform know that it is a linear operator? [duplicate]

I have the following issue with FourierTransform, Fourier transform doesn't seem to know it is a linear operator. ...
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 ...
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 ...
315 views

Issues with zero frequency component in discrete Fourier transform [closed]

I'm having trouble with the Fourier function at the moment. I'm solving a set of differential equations with NDSolve, then need to extract the spectrum associated with the curve below: So i use table ...
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 ...
335 views

Fourier Coefficients in Mathematica [duplicate]

I'm calculating Fourier Coefficients by hand and trying to verify them in Mathematica. However, in Mathematica I get them wrong by a factor of 2. Is there some part of the Mathematica functions I'm ...
251 views

DFT: Fourier Plot Not Giving Expected Result

I'm trying use Mathematica to compute the Discrete Fourier Transform (DFT) of a table of data points and then plot the result. As a test run, I took values from the function $x=f(t)=\sin(2\pi t)$ for ...
711 views

Precision while calculating Fourier transform

I'm trying to understand how precision works in Mathematica. Particularly I'm calculating discrete Fourier transform using the Fourier function and calculating it "...
219 views

341 views

Plotting amplitude spectra of modulated message signal

I'm trying to plot the amplitude spectrum of the modulated message signal, I have managed to plot it by working through the maths, expanding out each trig function, and then drawing onto a graph ...