Question

What is the necessary and sufficient condition for a second order filter that no zero-input overflow limit cycles occur?

(a) |a1|+|a2|=1

(b) |a1|+|a2|>1

(c) |a1|+|a2|<1

(d) None of the mentioned

I had been asked this question in an interview for job.

I want to ask this question from Round Off Effects in Digital Filters topic in section Digital Filters Design of Digital Signal Processing

Answer 1

The correct answer is (c) |a1|+|a2|<1

To explain: It can be easily shown that a necessary and sufficient condition for ensuring that no zero-input overflow limit cycles occur is |a1|+|a2|<1

which is extremely restrictive and hence an unreasonable constraint to impose on any second order section.