Question

If the contour is a circle of radius r and the zk are N equally spaced points, then what is the value of zk?

(a) re^-j2πkn/N

(b) re^jπkn/N

(c) re^j2πkn

(d) re^j2πkn/N

I got this question in exam.

My question is taken from Linear Filtering Approach to Computation of DFT in section DFT Efficient Computation – Fast Fourier Transform Algorithms of Digital Signal Processing

Answer 1

Right option is (d) re^j2πkn/N

The explanation is: We know that, if the contour is a circle of radius r and the zk are N equally spaced points, then what is the value of zk is given by re^j2πkn/N