Question

What is the causal inverse of the FIR system with impulse response h(n)=δ(n)-aδ(n-1)?

(a) δ(n)-aδ(n-1)

(b) δ(n)+aδ(n-1)

(c) a^-n

(d) a^n

The question was posed to me in a job interview.

Origin of the question is Inverse Systems and Deconvolution topic in portion Frequency Analysis of Signals and Systems of Digital Signal Processing

Answer 1

The correct option is (d) a^n

To elaborate: Given h(n)= δ(n)-aδ(n-1)

Since h(0)=1, h(1)=-a and h(n)=0 for n≥a, we have

hI(0)=1/h(0)=1.

and

hI(n)=-ahI(n-1) for n≥1

Consequently, hI(1)=a, hI(2)=a^2,….hI(n)=a^n

Which corresponds to a causal IIR system as expected.