Someone asked me about the advantage(s) of fast Fourier Transform in civil engineering programs?! or
What is the application of the Fourier series in engineering programming?
Can you help me or give me a clue? I've been searching google, but do not find an explanation. I was looking for an example to find out what's happening in the algorithm.
Remark: I know that the Fourier Transform is a function.
Fast Fourier Transform is an algorithm.
It would help to explain what "fast" means. Suppose I compute an FT with power-of-two length $N=2^m$. What's the arithmetic complexity? I'll consider $1$-dimensional FTs for simplicity. We know FFT algorithms that get it as low as $O(N\log N)$, which you can prove by divide & conquer; whether we can beat that is an open question. Without FFT techniques, a DFT takes $O(N^2)$ time.