Question

 A system is defined by its impulse response [ ] 2 2 ( ) n h n u n = − . Discuss whether the system is stable, causal, or unstable and non-causal? Support your answer? (5) 

Answer 1

A system is defined by its impluse response $h(n)=2^nu(n-2)$ . The system is instable and non-casual

Let $S= \sum^{\infin}_{- \infin}|h(n)|= \sum^{\infin}_{- \infin} 2^nu(n-2) = \sum^{\infin}_{- \infin}2^n=2+4+8+...= \infin$

Therefore the system is not stable.

A discrete-time LTI system is casual if and only if h(n) =0, n<0

For the given impulse response we have $h(-1)=2^{-1} \not=0$