Cooley-tukey fft algorithm

1. How does Cooley Tukey work?
2. What problem does the Cooley Tukey fast Fourier transform algorithm solve?
3. Is Cooley Tukey fast Fourier transform divide and conquer?
4. What are algorithms of FFT?

How does Cooley Tukey work?

in terms of N₁ smaller DFTs of sizes N₂, recursively, to reduce the computation time to O(N log N) for highly composite N (smooth numbers). Because of the algorithm's importance, specific variants and implementation styles have become known by their own names, as described below.

What problem does the Cooley Tukey fast Fourier transform algorithm solve?

The Cooley Tukey algorithm is a Fast Fourier transform algorithm that helps to retrieve the frequency components present in the signal. Also, the Cooley Tukey algorithm is fast as compared to DFT. The time complexity of a DFT is O (N^2) while Cooley Tukey FFT time complexity is O (N log N).

Is Cooley Tukey fast Fourier transform divide and conquer?

Fast Fourier Transform (FFT)

The FFT algorithm is an O(nlg n) divide and conquer algorithm for DFT, used by Gauss circa 1805, and popularized by Cooley and Turkey and 1965.

What are algorithms of FFT?

The FFT algorithm is one of the heavily used in many DSP applications. It is used whenever the signal needs to be processed in the spectral, or frequency domain. It is so efficient to implement, that sometimes even FIR filtering functions are performed using an FFT.