Question

If H(z) is the system function of an LTI system and HI(z) is the system function of the inverse LTI system, then which of the following is true?

(a) H(z)*HI(z)=1

(b) H(z)*HI(z)=δ(n)

(c) H(z).HI(z)=1

(d) H(z).HI(z)=δ(n)

I have been asked this question by my college professor while I was bunking the class.

Enquiry is from FIR Least Squares Inverse Filters topic in section Digital Filters Design of Digital Signal Processing

Answer 1

Correct choice is (c) H(z).HI(z)=1

Easiest explanation: The inverse to a linear time invariant system with impulse response h(n) and system function H(z) is defined as the system whose impulse response is hI(n) and system function HI(z), satisfy the following condition

H(z).HI(z)=1.