Question

fast fourier transform, dit, N=18 (use N=p1q1 notation used in oppenheim textbook).

for N =18 use p1 =3 and p2 = 6 (3 sequences of length 6) show all steps and show how to change q1 to p2p3 where p2 = 3 and p3 = 2

Answer 1

The question is a little bit confusing. By understanding in overview I'm giving these references and explanation

It's just a different way of doing FFT using smaller problems and which uses the Prime Factor Mapping algorithm.

Refer book Fast Fourier Transform: Algorithms and Applications by K.R. Rao, D.N. Kim, and J.J. Hwang

https://en.wikipedia.org/wiki/Prime-factor_FFT_algorithm

N = p1q1 where p1 and q1 are coprime numbers

The re-indexing in n domain is called Good's mapping and in k domain is called Thomas mapping (CRT mapping)

This operation uses modular multiplicative inverse which exploits the periodicity property of complex exponentials in DFT