Question

In the equation SQNR = 6.02b + 16.81 – \(20log_{10} ⁡\frac{R}{σ_x}\), for R = 6σx the equation becomes?

(a) SQNR = 6.02b-1.25 dB

(b) SQNR = 6.87b-1.55 dB

(c) SQNR = 6.02b+1.25 dB

(d) SQNR = 6.87b+1.25 dB

I got this question in examination.

This interesting question is from Analysis of Quantization Errors in portion Discrete Time Systems Implementation of Digital Signal Processing

Answer 1

Correct option is (c) SQNR = 6.02b+1.25 dB

The explanation: For example, if we assume that x(n) is Gaussian distributed and the range o f the quantizer extends from -3σx to 3σx (i.e., R = 6σx), then less than 3 out o f every 1000 input signal amplitudes would result in an overload on the average. For R = 6σx, then the equation becomes

SQNR = 6.02b+1.25 dB.