2. Time-Domain Representations of LTI Systems

2.7 Relations Between LTISystem Properties and the Impulse Response1. The system is causal, since h[n] = 0 for n < 0.2. The system is not memoryless, since h[n] 0 for n > 0.3. Stability : Checking whether the impulse response is absolutely summable?kkh[ k] if and only if < 1k k 0 k 0◆ Special case : A system can be unstable even though the impulseresponse has a finite value.1. Ideal integrator :2. Ideal accumulator : ty ( t)x()d(2.29)Input : x() = (), then theoutput is y(t) = h(t) = u(t).h(t) is not absolutely integrableIdeal integrator is not stable!nk y[ n] x[ k]Impulse response : h[n] = u[n]h[n] is not absolutely summableIdeal accumulator is not stable!Time-Domain Representations ofLTI Systems44