1.

What is the inverse of the system with impulse response h(n)=(1/2)^nu(n)?(a) δ(n)+1/2 δ(n-1)(b) δ(n)-1/2 δ(n-1)(c) δ(n)-1/2 δ(n+1)(d) δ(n)+1/2 δ(n+1)The question was asked in an online interview.Enquiry is from Inverse Systems and Deconvolution topic in section Frequency Analysis of Signals and Systems of Digital Signal Processing

Answer»

Right option is (b) δ(n)-1/2 δ(n-1)

Explanation: Given impulse RESPONSE is h(n)=(1/2)^nu(n)

The system function corresponding to h(n) is

H(z)=\(\frac{1}{1-\frac{1}{2} z^{-1}}\) ROC:|z|>1/2

This system is both stable and CAUSAL. Since H(z) is all POLE system, its inverse is FIR and is given by the system function

HI(z)=\(1-\frac{1}{2} z^{-1}\)

Hence its impulse response is δ(n)-1/2 δ(n-1).



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