TIFR ECE 2013 | Question: 2

Question

The output $\{y(n)\}$ of a discrete time system with input $\{x(n)\}$ is given by
\[
y(n)=\sum_{k=0}^{N-1} a^{k} x(n-k) .
\]
The difference equation for the inverse system is given by

• A. $y(n)=x(n)-a x(n-1)$
• B. $y(n)-a^{N} y(n-N)=x(n)-a x(n-1)$
• C. If $|a|<1$, then the answer is $(a)$ above, otherwise the inverse does not exist
• D. If $|a|<1$, then the answer is $(b)$ above, otherwise the inverse does not exist
• E. None of the above