Question

By combining \(\Delta=\frac{R}{2^{b+1}}\) with \(P_n=\sigma_e^2=\Delta^2/12\) and substituting the result into SQNR = 10 \(log_{10}⁡ \frac{P_x}{P_n}\), what is the final expression for SQNR = ?

(a) 6.02b + 16.81 + \(20log_{10}\frac{R}{σ_x}\)

(b) 6.02b + 16.81 – \(20log_{10}⁡ \frac{R}{σ_x}\)

(c) 6.02b – 16.81 – \(20log_{10}⁡ \frac{R}{σ_x}\)

(d) 6.02b – 16.81 – \(20log_{10}⁡ \frac{R}{σ_x}\)

I got this question in a job interview.

I need to ask this question from Analysis of Quantization Errors topic in section Discrete Time Systems Implementation of Digital Signal Processing

Answer 1

Correct option is (b) 6.02b + 16.81 – \(20log_{10}⁡ \frac{R}{σ_x}\)

To elaborate: SQNR = \(10 log_{10}⁡\frac{P_x}{P_n}=20 log_{10} \frac{⁡σ_x}{σ_e}\)

= 6.02b + 16.81 – ⁡\(20 log_{10}\frac{R}{σ_x}\)dB.