Question

Zero input limit cycles occur from non-zero initial conditions with the input x(n)=0.

(a) True

(b) False

I got this question at a job interview.

This intriguing question comes from Round Off Effects in Digital Filters topic in chapter Digital Filters Design of Digital Signal Processing

Answer 1

The correct answer is (a) True

For explanation: When the input sequence x(n) to the filter becomes zero, the output of the filter then, after a number of iterations, enters into the limit cycle. The output remains in the limit cycle until another input of sufficient size is applied that drives the system out of the limit cycle. Similarly, zero input limit cycles occur from non-zero initial conditions with the input x(n)=0.