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^nThe 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

What is the causal inverse of the FIR system with impulse response h(n

1.	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^nThe 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» 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.

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