Question

What is the average power of the discrete time periodic signal x(n) with period N?

(a) \(\frac{1}{N} \sum_{n=0}^{N}|x(n)|\)

(b) \(\frac{1}{N} \sum_{n=0}^{N-1}|x(n)|\)

(c) \(\frac{1}{N} \sum_{n=0}^{N}|x(n)|^2\)

(d) \(\frac{1}{N} \sum_{n=0}^{N-1}|x(n)|^2 \)

This question was addressed to me during an internship interview.

I need to ask this question from Frequency Analysis of Discrete Time Signal in section Frequency Analysis of Signals and Systems of Digital Signal Processing

Answer 1

The correct option is (d) \(\frac{1}{N} \sum_{n=0}^{N-1}|x(n)|^2 \)

Explanation: Let us consider a discrete time periodic signal x(n) with period N.

The average power of that signal is given as

Px=\(\frac{1}{N} \sum_{n=0}^{N-1}|x(n)|^2\)