Question

What is the equation to compute the values of the z-transform of x(n) at a set of points {zk}?

(a) \(\sum_{n=0}^{N-1} x(n) z_k ^n\), k=0,1,2…L-1

(b) \(\sum_{n=0}^{N-1} x(n) z_{-k}^{-n}\), k=0,1,2…L-1

(c) \(\sum_{n=0}^{N-1} x(n) z_k^{-n}\), k=0,1,2…L-1

(d) None of the mentioned

This question was posed to me in examination.

This interesting question is from Linear Filtering Approach to Computation of DFT in division DFT Efficient Computation – Fast Fourier Transform Algorithms of Digital Signal Processing

Answer 1

Correct option is (c) \(\sum_{n=0}^{N-1} x(n) z_k^{-n}\), k=0,1,2…L-1

The explanation: According to the Chirp-z transform algorithm, if we wish to compute the values of the z-transform of x(n) at a set of points {zk}. Then,

X(zk)=\(\sum_{n=0}^{N-1} x(n) z_k^{-n}\), k=0,1,2…L-1