# Questions tagged [fast-fourier-transform]

Use this tag for questions related to the fast Fourier transform, an algorithm that samples a signal over a period of time (or space) and divides it into its frequency components.

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13 views

### DFT of a series of RC exponentials

Context: I'm trying use matlab to apply a single-pole filter to a time-domain ramp waveform that is generated by a sequence of time-shifted "RC steps" that are added together. The time domain voltage ...
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### Fourier tranform of the derivative

I have been recently studing Fourier transform and there is a proposition that says: If $\lim \limits_{x \to\infty}xf(x)=\lim\limits_{{x}\to -\infty}xf(x)=0$ then $$\hat{f'}(z)=-iz\hat{f}(z)$$ and ...
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### Fourier odd and even extension of descending steps function

Can anybody help me find even and odd extension of the descending steps function if $f(x)$ be: \begin{cases} f(x)= 1 & x\in[0,1]\\ f(x)= (0.5) & x\in[1,2] \end{cases}
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### Should DFT of cosine function be infinite at its frequency?

The Fourier transform of the cosine function is an infinite spike (Dirac delta function) at the frequency of the cosine wave. But it seems most DFT programs give a finite spike corresponding to the ...
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### Discrete Fourier transform of sampled sin function nothing like continuous?

So I'm a little confused about what is going on with the discrete Fourier transform. I tested out discrete Fourier transform with a little python script on a sin function ...
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### Fourier transform of delta(dirac) function-multiplication with exp function

I am trying to find an integral of multiplication exponential function with a delta function. I know a property of delta function that if I would like to take the integral of the multiplication delta ...
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### Informations about Fourier Transform for a Python project (sound manipulation)

I have a project in Python with a friend where we want to manipulate music sound, and we'll need Fourier Transforms, so I made research online and wanted to know if I understand correctly the concepts....
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### Most efficient method to find peak frequency of an FFT

I'm using a real to complex fft to get the peak frequency of a signal. What I want to know is the most efficient way to find the index of that peak. I currently use im^2 + re^2 and compare to the ...
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### fft algorithm - twidle multiplication

im trying to understand how fft(fast fourier transform) algorithm work and after watching several videos i couldn't understand why there is multiplication with Wn in this specific places and why the ...
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### Not getting expected results with FFT

So I made this virtual car that moves at a velocity that is the sum of three different sine waves (whose individual frequencies I know). I constructed this velocity time graph Then I perform a FFT on ...
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### Discrete Hartley Transform when N=8

Hi I am currently studying FHT Algorithm but have a hard time to grasp it. I want to calculate FHT when N=8. http://mathworld.wolfram.com/HartleyTransform.html thanks to (19) of the upper link, the ...
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### Using fft() in Matlab

I have a function defined like: $$x(t)=2e^{-\frac{r}{2}t}\sin\left(\frac{1}{2}\sqrt{16\pi^2-r^2}\cdot t\right)\left(\frac{\Theta(t)}{\sqrt{16\pi^2-r^2}}\right)$$ Where $\Theta(t)$ is the Heaviside ...
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### How to assess the convergence of a time series towards a periodic signal and assess the sufficiency of the sample size?

I have a sampled temporal signal, result of a transient fluid simulation. At the beginning the flow is being established, so the first few seconds of signal should be ignored (question : is there a ...
116 views

### Fourier coefficients computed by MATLAB fft function don't match exact ones

I am trying to find out the Fourier coefficients of function $\cos\left(\frac{\pi x}{7}\right)$ on the interval of $[0\,,\,7]$ by using MATLAB built-in function fft in order to verify my own DFT and ...
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### Simple DFT Coefficients => Amplitude/Frequencies

Im trying on DFT and FFT in Python with numpy and pyplot. My Sample Vector is x = np.array([1,2,4,3] The DFT coefficients for that vector are ...
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### Compute Transfer Function from FFT of Input and Output

I tried the method described in a previous answer (https://math.stackexchange.com/a/718856/451691) to compute the transfer function of a system I am studying, where: In(t) = a(t); Out(t) = b(t) I ...
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### Low Pass Filter using FFT up to the Nth overtone

I'm writing a program in c# that uses Meta.Numerics to calculate the FFT of a signal recorded during one cycle. The overtones are presented as complex numbers. Now I would like to reconstruct the ...
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### Discorrespondence between Continous Fourier Transform and Discrete Fourier Transform

My goal is to use a deconvolution method to extract a desired signal (delta peak) out of a convoluted measured function. My problem at first concerns the discrete Fourier Transform (DFT) or FFT ...
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### Use of FFT with a different definition of multiplication operator

FFT enables us to perform multiplication of polynomials in O(nlogn), where "multiplication" is the standard multiplication over the complex numbers. Is there a general procedure to extend this use of ...
59 views

### What does the imaginary part of a set of polar coordinates represent before and after funning an FFT?

My colleague and I are trying to learn stuff that is way above our pay grade. We are curious about the nature of the FFT. We realize that we will most likely not understand the inner workings of the ...
338 views

### How to Prove the Fourier Transform of Vertical Line Mathematically?

I've tried to do Fourier transform in Matlab of vertical line. Basically, I make matrix A having size 100x100 and give the value 1s in certain number of coloumn vector, whereas the others is 0s. Here ...
234 views

### Optimization for getting amplitude of FFT results for real signals

I need to compute amplitude of FFT result for real signals, which means that I don't need the precise result of FFT or phase information of the result. So I think I don't need to implement the ...
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### Why, traditionally, does FFT use complex numbers as a wrapper for magnitude and phase?

I've read questions like this one, this one, and this one which ask why we use complex numbers instead of real numbers, and that's one half of the question, but the other half, which I've never seen ...
496 views

### NTT for fast multiplication of polynomials over a finite field, and the connection to polynomial evaluation

Trying to code NTT and INTT in order to have faster polynomial multiplication. That has been extremely mind boggling for me. The polynomials are over a finite field $GF(q)$. I've already coded some ...
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### Analysis of a linear increase in standard divination. What might cause a linear increase in floating point error?

Background: We are doing mathematical transformations on large matrices of inline fraunhofer holography data (the nature of this isn't really important, but if you are curious, essentially it is a ...
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### Chossing a prime for fft of size $2^n$

I have a $p$ degree polynomial where $p$ is prime, I want to find the value of this polynomial at all points from $1$ to $p-1$,to make the fft on this polynomial easier I padded it with zeroes up to ...
I got confused in the FFT butterfly diagram. Can someone please help me understand it? If I have the vector $x = (-3, -2, -1, 0, 1, 2, 3, 4)$, and I want to apply FFT to it using the Butterfly ...