Question

What is the dead band of a single pole filter with a pole at 3/4 and represented by 4 bits?

(a) (-1/2,1/2)

(b) (-1/8,1/8)

(c) (-1/4,1/4)

(d) (-1/16,1/16)

I got this question in an interview for job.

This interesting question is from Round Off Effects in Digital Filters topic in section Digital Filters Design of Digital Signal Processing

Answer 1

Right choice is (b) (-1/8,1/8)

Easiest explanation: We know that

|v(n-1)| ≤ \(\frac{(\frac{1}{2}).2^{-b}}{1-|a|}\)

Given |a|=3/4 and b=4 => |v(n-1)| ≤ 1/8=> The dead band is (-1/8,1/8).