问答题
线性系统由图的子系统组合而成。设子系统的冲激响应分别为h
1
(t)=δ(t-1)，h
2
(t)=δ(t)-δ(t-3)。求组合系统的冲激响应。
【正确答案】
【答案解析】解 由图可知组合系统在e(t)激励下的响应为
r(t)=e(t)+h 1 (t)*e(t)+[h 1 (t)*h 2 (t)]*e(t)=e(t)*δ(t)+h 1 (t)*e(t)+[h 1 (t)*h 2 (t)]*e(t)=e(t)*[δ(t)+h 1 (t)+h 1 (t)*h 2 (t)]=e(t)*h(t)
故组合系统的冲激响应为
h(t)=δ(t)+h 1 (t)+h 1 (t)*h 2 (t)=δ(t)+δ(t-1)+δ(t-1)*[δ(t)-δ(t-3)]=δ(t)+2δ(t-1)-δ(t-4)
r(t)=e(t)+h 1 (t)*e(t)+[h 1 (t)*h 2 (t)]*e(t)=e(t)*δ(t)+h 1 (t)*e(t)+[h 1 (t)*h 2 (t)]*e(t)=e(t)*[δ(t)+h 1 (t)+h 1 (t)*h 2 (t)]=e(t)*h(t)
故组合系统的冲激响应为
h(t)=δ(t)+h 1 (t)+h 1 (t)*h 2 (t)=δ(t)+δ(t-1)+δ(t-1)*[δ(t)-δ(t-3)]=δ(t)+2δ(t-1)-δ(t-4)