Question

If h(n) is the impulse response of an LTI system and hI(n) is the impulse response of the inverse LTI system, then which of the following is true?

(a) h(n).hI(n)=1

(b) h(n).hI(n)=δ(n)

(c) h(n)*hI(n)=1

(d) h(n)*hI(n)=δ(n)

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I want to ask this question from FIR Least Squares Inverse Filters topic in portion Digital Filters Design of Digital Signal Processing

Answer 1

Right option is (d) h(n)*hI(n)=δ(n)

The explanation: The inverse to a linear time invariant system with impulse response h(n) is defined as the system whose impulse response is hI(n), satisfy the following condition h(n)*hI(n)=δ(n).