# 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.

220 questions
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### How does FFT work?

For five years I tried to understand how Fourier transform works. Read a lot of articles, but nobody could explain it in simple terms. Two weeks ago I stumbled upon the video about a 100 years old ...
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### Value Proposition of Fourier Analysis?

I am a software engineer trying to wrap his head around Fast Fourier Transform (FFT). Specifically, I need to implement it as part of some software I am writing. Now I can handle the implementation of ...
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### Intuition of fft over time to frequency

I understand how FFT (DFT) works. It acts as a change of basis. However, while many websites describe fft as a method that convert time domain stuff to frequency domain stuff, I still do not know why ...
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### How to get the frequency of a time-domain signal with limited sample length?

Let's say there is a signal who only has one peak in its power spectrum. I would like to know the frequency at which the peak is (the magnitude of power is not important to me). But I only have very ...
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### Is it possible to solve the following PDE without using Fourier transform?

Solve the following non-homogenous heat equation:$$\frac{\partial u}{\partial t} = a^2 \frac{\partial ^2 u}{\partial x^2} + \epsilon \sin(k_0x)$$ on the domain $-\infty \lt x \lt \infty$, with ...
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### How to interpret the results of a Discrete Fourier Transform

I'm trying to understand the Discrete Fourier Transform so that I can understand the Fast Fourier Transform so that I can write a program to calculate it. I know that there are existing libraries that ...
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### Parseval identity in FFT

I was recreating in Matlab a certain function using FFT. In particular I was interesting in knowing how modes are sufficient to approximate quite well my function. To do that, I calculate the norm ...
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### Approximate Factorization of a Natural Number

I'm implementing the Cooley-Tukey algorithm for computing Discrete Fourier transforms. It so happens that it breaks down a problem of size $n = pq$ into $p$ chunks of size $q$. Given that factoring ...
### What is $\sin(\frac{\pi}{2}-\frac{n\pi}{2})$ equal to?
I'm having huge trouble with figuring out fourier series as soon as I'm not dealing with a really simple function. I found a solution to my problem (fourier series for $|cos(x)|$, I'm troubled by the ...