Question

A discrete time system has impulse response, $h\left(n\right)=b^{n}u(n+1),|b|<1$. Which one of the following statement is correct ?

• A. unstable, causal and has memory
• B. unstable, non-causal and memory less.
• C. stable, causal and memory less.
• D. stable, non- causal and has memory

Answer 1

The correct option is D stable, non- causal and has memory

$h\left(n\right)=b^{n}u(n+1),|b|<1$

It is stable because,

$\sum _{n=-\infty }^{\infty }h\left(n\right)=\sum _{n=-1}^{\infty }{b}^{n}isfinite$

It is non - causal because h(n) exists from $n=-1ton=\infty$.
It has memory because h(n) is depending upon u(n +1).