Question

What is the dead band of a single pole filter with a pole at 1/2 and represented by 4 bits?

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

(b) (-1/4,1/4)

(c) (-1/8,1/8)

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

I have been asked this question during an online exam.

My enquiry is from Round Off Effects in Digital Filters topic in division Digital Filters Design of Digital Signal Processing

Answer 1

The correct choice is (d) (-1/16,1/16)

The explanation is: We know that

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

Given |a|=1/2 and b=4 => |v(n-1)| ≤ 1/16=> The dead band is (-1/16,1/16).