Linked Questions

23
votes
3answers
5k views

How to make Fourier behave like FourierTransform?

I'm not very experienced with Fourier Transforms, so there may be something inherently wrong with attempting to do this, but how can I make the discrete Fourier behave like the continuous ...
22
votes
6answers
23k views

How do you find the frequency and amplitude from Fourier?

Edit This is a popular question with several answers. This edit organises the answers and gives links. Fourier just gives y values (ordinates) if you wish to read off frequencies and amplitudes you ...
20
votes
4answers
6k views

How to calculate the Fourier Transform of a Gaussian pulse with a nonlinear chirp: Cos[ t + Exp[t^2] ]?

I have an optical pulse in time domain: Exp[-t^2] Cos[50 t - Exp[-2 t^2] 8 π]. The figure of this formula is I hope to calculate the Fourier Transform of this ...
10
votes
1answer
683 views

finding Frequency of Sinewave data using Fourier

CONTEXT I read 5 different related posts but I do not understand how to interpret mathematica's output for my situation. ...
9
votes
2answers
423 views

Frequency of ticks in mechanical watches

I'm looking to find the frequency of a relatively large dataset (or a relatively short audio file) of a repeating sound, like so: Here are the original files, for those willing to play. :) eta2412 ...
5
votes
1answer
2k views

Differences between FFT and analytical Fourier Transform

In MATLAB, if I perform an FFT on a simple Gaussian spot with a phase grating: ...
4
votes
1answer
239 views

Comparing ordinates between FourierTransform and Fourier

I have a test function ff[t_] := Exp[-t^2 - t]. I have calculated the Fourier transform with FourierTransform: ...
4
votes
1answer
2k views

Why Fourier transform is symmetric no matter what interval I choose? [duplicate]

I'm solving a vibration problem. After solving two systems of ODEs (one valid in 0-0.1 and the other in 0.1-1) I get the plot of 3 functions, one of them is this, the plot of the variable $y_w$ (Image ...
3
votes
2answers
327 views

Discrete Fourier Transform - Inadequate precision and wrong peak positions

I have a small problem with a piece of code. I searched the site but was not able to find an answer to my specific question. I am trying a quick test of the Fourier capabilities (on lists) of ...
3
votes
1answer
3k views

Using mathematica to take fourier transform of data

I'm trying to use Mathematica to take a discrete Fourier transform of 68 data points (0 to 67) to perform further analysis. My data points, when plotted, look like this: Pretty straightforward. Now,...
3
votes
1answer
50 views

How does the Fourier transform take its input?

I'm using the Fourier command and I'm wondering how does it take its imput. I know that it takes a list of numbers representing a function of time and it gives back a list of numbers representing a ...
3
votes
1answer
379 views

Fourier Transform accelerogram seismic

I have a seismic accelerogram. I tried to apply the Fourier Transform to interpolate function, but dosn't work. So, i applied the ...
2
votes
2answers
162 views

Figuring out the frequency components using FFT [duplicate]

The function defined below has three frequencies 2, 4 and 10. How to use the Fourier transform (FFT) to show these frequencies? ...
2
votes
1answer
491 views

How to find the Fourier Transform of a list?

I have a list (list) in the form of {x,y} as ...
2
votes
1answer
149 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
105 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
0answers
76 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 ...
1
vote
3answers
365 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
503 views

DFT: why are frequencies mirrored around the frequency axis?

I want to apply Mathematica's DFT procedure, Fourier[], to a Gaussian. Why a Gaussian? Because I know the analytical result. So I define ...
1
vote
1answer
319 views

Get frequency axis in Fourier transform (and save them)

I am trying to get the Fourier transform of a light-curve (with an even number of points, 300, and equally spaced in time, 6.9 seconds) and my problem is to get the frequency on the x-axis. I can ...
1
vote
2answers
365 views

Parseval identity in one side Fourier Transform

Is there any posibility to apply Parseval identity(energy in time domain is equal to freq. domain) on One/Single-side Fourier transform? In other word for "standard" FT the test Mathematica can be <...
1
vote
2answers
219 views

DataRange in plotting Fourier

I'm trying to estimate a frequency spectrum of a given discrete function. I have a file which is filled of values of Sine-function $sin(t)$, where $t$ runs from $0.0$ to $100.0$ and a discrete step is ...
1
vote
1answer
72 views

Why does Mathematica Fourier transform of finite sequence of numbers require parameters?

I apologize if this is a basic question, but here goes: The Discrete Fourier transform of a sequence of N complex numbers is uniquely defined by eq.1 in this wiki page, https://en.wikipedia.org/wiki/...
1
vote
1answer
77 views

Fast method for numerical integral (Fouriertransform?)

I want to numerically compute following integral (as fast as possible): \begin{equation} f(x) = \left| \int e^{ \mathrm{i} p x / 2} f(p) \ \mathrm{d}p\right|^2 , \end{equation} where $f(p)$ is given ...
1
vote
0answers
36 views

Taking Fourier transform with WolframAlpha gives unexpected result [duplicate]

I have noticed that WolframAlpha's definition of the Fourier Transform is different than the one in my book of formulas. In my book the Fourier transform of $f(t)$ is defined as: $$\int_{-\infty}^{\...
1
vote
1answer
91 views

Finding frequency of oscillation of an particle by Fourier analysis of the trajectory [duplicate]

I am trying to find the resonant frequency of a particle by Fourier analysis of the trajectory. Here is the data file. ...
1
vote
0answers
74 views

Taking numerical Laplace transform of a tabulated data with Mathematica?

I am relatively new to the use of Mathematica in the context of numerical evaluations, therefore I would greatly appreciate a detailed answer and would like to express my gratitude towards any help in ...
1
vote
0answers
216 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 ...
0
votes
1answer
157 views

Finding frequency from Fourier transform [closed]

I tried to find frequency using Fourier Transform, but notice that my code have some mistakes which I can't find. So, my code is below: ...
0
votes
1answer
5k views

Discrete Fourier Transform: help on how to convert x axis in to the frequency when I have a set of data samples [duplicate]

I have a huge data set (400000 sample) and when I plot them ListLinePlot[Au4, PlotRange -> {All, All}] I used the following code to Fourier transform it <...

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