26k 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 ...
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 ...
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 ...
421 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 ...
575 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 ...
365 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 ...
202 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? ...
395 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 <...
231 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 ...
387 views

### Wrong frequency in Fourier

I have a file, filled with data like this: As you can see the approximate frequency is about $5/1000 = 0.005$, then angular frequency is about $2 \pi \times 0.005 \approx 0.03$. Then I use discrete ...
750 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. ...
3k views

### Differences between FFT and analytical Fourier Transform

In MATLAB, if I perform an FFT on a simple Gaussian spot with a phase grating: ...
269 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: ...
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 ...
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### 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 ...
4k 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,...
395 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 ...
189 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 ...
716 views

### How to find the Fourier Transform of a list?

I have a list (list) in the form of {x,y} as ...
111 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. ...
79 views

### Fast method for numerical integral (Fouriertransform?)

I want to numerically compute following integral (as fast as possible): $$f(x) = \left| \int e^{ \mathrm{i} p x / 2} f(p) \ \mathrm{d}p\right|^2 ,$$ where $f(p)$ is given ...
109 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. ...
470 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 ...
520 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 ...
73 views

### How can I make an FFT in Mathematica using data from a file? [closed]

I need to calculate the seismic moment of an earthquake data, but I don't know how the FFT is applied in some data, my data is a plain text that I must import it to Mathematica ...
120 views

### Using Fourier to get the numerical FT of a Gaussian [duplicate]

I've been trying to find the FT of a more complicated function, but it seems my method is wrong. To check, I tried to calculate the FT of a Gaussian numerically. This is what I did: ...
300 views

### Discrete fourier transform and convolution — scaling factor?

I am trying to convolve a square wave (a diffraction grating phgrating with slits size \[CapitalLambda]) with a point spread ...
126 views

### Identifying the three frequencies using fourier transform

The following simple function has clearly three frequency components: ...
104 views

### How to fit one function into the form of another?

I have a slightly complicated periodic function of one variable t, say g[t]. I want to do a least squares fit of that function ...
200 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: ...
228 views

### Periodogram local maximum

I want to find dominant frequencies of periodogram exactly. ...
358 views

### Ideal/Brick wall Low/High-pass filters: Fourier approach not working

I am trying to take a signal (as a list) and separate it into the low frequency and high frequency parts around some split frequency f. Given that what little signal processing I ever studied is now ...
1k views

### FFT of data to obtain resonance frequencies and correct amplitudes

I have often to do with experimental data (with a certain length and given sampling frequency) where I obtain trajetories of moving objects in 2d. Then I am interested to find out what the ...
206 views

### Frequencies doubled in fourier transform [duplicate]

With this code I get a nice plot of the Fourier transform, but the frequencies are doubled. By this I mean that when using a sine wave I generated at 220 Hz, the plot gives me a single peak at 440 Hz. ...
6k 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 <...
100 views

### Why does Mathematica Fourier transform of finite sequence of numbers require parameters? [closed]

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/...
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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 ...
38 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}^{\...
120 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 ...
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 ...
54 views

### Finding Fourier transform of a quantity v/s theta (0 to 360 degrees)

I have a physical quantity (experimentally measured) lets say T whose variation I have measured with angle (theta in degrees). I want to find out the Fourier components of this quantity with respect ...
66 views

### Frequencies for Fourier coefficients [duplicate]

I have been given the task of calculating the frequencies to which the fourier coefficients correspond. So my input is a discrete signal [1,4,0,1], which gives me <...