Question

In the equation SQNR = 10 ⁡\(log_{10}\frac{P_x}{P_n}\), what are the expressions of Px and Pn?

(a) \(P_x=\sigma^2=E[x^2 (n)] \,and\, P_n=\sigma_e^2=E[e_q^2 (n)]\)

(b) \(P_x=\sigma^2=E[x^2 (n)] \,and\, P_n=\sigma_e^2=E[e_q^3 (n)]\)

(c) \(P_x=\sigma^2=E[x^3 (n)] \,and\, P_n=\sigma_e^2=E[e_q^2 (n)]\)

(d) None of the mentioned

I had been asked this question during an online exam.

This intriguing question comes from Analysis of Quantization Errors in chapter Discrete Time Systems Implementation of Digital Signal Processing

Answer 1

The correct answer is (a) \(P_x=\sigma^2=E[x^2 (n)] \,and\, P_n=\sigma_e^2=E[e_q^2 (n)]\)

Explanation: In the equation SQNR = \(10 log_{10}⁡ \frac{P_x}{P_n}\), then the terms \(P_x=\sigma^2=E[x^2 (n)]\) and \(P_n=\sigma_e^2=E[e_q^2 (n)]\).