Recursive version of DFT as presented in Cooley-Tukey paper

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

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.

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 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).