Question

The N^th rot of unity WN is given as ______________

(a) e^j2πN

(b) e^-j2πN

(c) e^-j2π/N

(d) e^j2π/N

I got this question in my homework.

My question is from Frequency Domain Sampling DFT topic in portion Discrete Fourier Transform – Properties and Applications of Digital Signal Processing

Answer 1

Correct answer is (c) e^-j2π/N

For explanation I would say: We know that the Discrete Fourier transform of a signal x(n) is given as X(k)=\(\sum_{n=0}^{N-1}x(n)e^{-j2πkn/N}=\sum_{n=0}^{N-1}x(n)W_N^{kn}\)

Thus we get N^th rot of unity WN=e^-j2π/N