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.

Filter by
Sorted by
Tagged with
2
votes
1answer
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] ...
2
votes
1answer
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[1] to x[3] is: ...
2
votes
1answer
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: ...
2
votes
1answer
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 ...
2
votes
1answer
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 ...
2
votes
1answer
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 ...
2
votes
1answer
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 ...
2
votes
1answer
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 ...
2
votes
1answer
517 views

Partial derivative with Dirac Delta as initial condition

I am trying to reproduce the Faynman-Kac results from this Wikipedia page: Faynman-Kac This is the equation that I am trying to solve: $$ \frac{\partial w(t,x)}{\partial t} = \frac{1}{2} \frac{\...
2
votes
1answer
67 views

FourierTransform a function doesn't give result when variable is 0

I am trying to get a Fourier Transform of a function. However it doesn' work when the variable is 0. I used Mathematica 8.0 on a Windows Server 2008 R2 system. The code is as follows: Defining ...
2
votes
1answer
46 views

Why I get negative values on using periodogram after Fourier analysis?

sorry for bothering you with this question today. I am trying to analyze wave data that was produced using a wave tank. The period used for the waves is 1.7s, the waves encountered an obstacle at some ...
2
votes
1answer
151 views

Implementing an anti-alliasing filter in Mathematica

I'm experimenting with FFT simulations. I'm generating transient data at the some sampling rate, down-sampling this (mimicking a device's behavior) to 2048 points. Then take the FFT using ...
2
votes
1answer
113 views

Discrete Fourier transformation from ASCII (for noob)

I am not familiar with Mathematica (I am a physicist programming in Fortran) and my knowledge of it is very limited, unfortunately. I would like to perform the Fourier trasform of a lightcurve which ...
2
votes
1answer
103 views

Fourier Transform of a symbolic expression

Hello I would like to do the Fourier Transform of H1'[t - L2[t]/c - L2primo[t]/c] I know that its transform has to be: ...
2
votes
1answer
92 views

Using ''Module' and 'Table' to Plot 'Fourier'

I'm trying to make a function that outputs a plot given a particular parameter, whilst using the Mathematica functions Module, Fourier, and Table. This is what I've come up with thus far. ...
2
votes
1answer
147 views

Reconstruct signal using InverseFourier [closed]

I start from a signal, I do discrete Fourier transform of the signal, and I want to get back this same signal doing a discrete inverse Fourier transform. However, when I do so, I do not obtain the ...
2
votes
1answer
156 views

Two different results for same symbolic integral

I am trying to compute the following integral $\int_0^\infty dk \frac{e^{i k a}}{k^2}[\sin(kb)-kb\cos(kb)]$ When computing it as-is, i.e, with the code ...
2
votes
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
votes
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
votes
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
votes
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
votes
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
votes
0answers
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 ...
2
votes
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
votes
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
votes
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
votes
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
votes
0answers
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 ...
2
votes
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
votes
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
votes
0answers
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 ...
2
votes
0answers
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. ...
2
votes
0answers
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. ...
2
votes
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
votes
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
votes
0answers
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 ...
2
votes
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 ...
2
votes
0answers
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 ...
1
vote
3answers
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 ...
1
vote
1answer
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 "...
1
vote
4answers
219 views

How to calculate the Fourier transform of Sinc[b (ω1 - ω2)]?

I would like to calculate the Fourier transform of Sinc[ b (ω1 - ω2)], but there are some problems as follows: My target is $\int _{-\infty }^{\infty }\int _{-\infty }^{\infty }\text{Sinc}(b (\...
1
vote
1answer
464 views

Fourier Transform With Noise

For the following function I need to do the following steps. Sin[2πt](1+0.2 Sin [6πt] + 0.1 Sin [8πt]) Plot the function. Generate a table of data points from this function with random noise ...
1
vote
2answers
1k views

Fourier series for rectangular wave incorrect, why?

I'm trying to get the fourier series function(s) to work for a square wave with duty cycles other than 50% ie rectangular wave. ...
1
vote
2answers
2k views

How to calculate FDCT

I'm new to Mathemtica and I'm trying to calculate Discrete Cosine Transformation FDCT. I found the FourierDCT built-in function, but not DCT, so I need to implement it. I have tried couple of ideas ...
1
vote
2answers
2k views

How to realize a Fourier Transform on a non-uniform sampling data

I have a non-uniform sampling data (in time domain) from a Michelson interference experiment, as shown in Fig 1. But it was not evenly sampled (the step length was not uniform), because of the ...
1
vote
3answers
191 views

Another way to calculate frequency from Fourier transform

I have some trouble with calculating frequency after Fourier transform. My code: ...
1
vote
2answers
78 views

Integral Transform of exponential function over the positive axes

How do you integrate $\int\limits_0^{\infty} e^{i \omega x}\ \mathrm dx$?
1
vote
2answers
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 ...
1
vote
1answer
230 views

Problem of Discrete Fourier?

I tried Fourier Transform for a range of figures. Firstly, I tried in this way. ...
1
vote
2answers
303 views

Why does InverseFourierTransform gives different result to doing it by hand? [duplicate]

When I can calculate an inverse fourier transform by the built-in function InverserFourierTransform, the result is different from what I calculate by definition ...