Question

5- Determine whether or not each of the following LTI systems with the given impulse response are memoryless: a) h(t) = 56(t- 1) b) h(t) = eT u(t) e) h[n] sinEn) d) h[n] = 26[n] 6- Determine whether or not each of the following LTI systems with the given impulse response are stable: a) h(t) = 2 b) h(t) = e2tu(t - 1) c) h[n] = 3"u[n] d) h[n] = cos(Tm)u[n] 7- Determine whether or not each of the following LTI systems with the given impulse response are causal: a) h(t) = 2cos(3t) b) h(t) = e'u(t- 2) c) h[n] = o[n + 1] + 28[n] + S[n -- 1]| d) h[n] = cos(an)u[3 -- n]

Answer 1

5) For memoryless system, there should be no time shift. Time shift is only present in a. Hence b, c and d are memoryless while a has got memory.

6) For a stable system at n = infinity, the impulse response should have a finite value. It should not be infinite. Only for c, the value is infinite for n = infinity. Hence c is unstable while a, b and d are stable.

7) For causal system, no coefficient in the system should be a function of t. However in b, the coefficient is a function of t. Hence b is non-causal while a, c and d are causal.