已知系统的冲激响应h(t)=e-2tu(t):

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已知系统的冲激响应h(t)=e-2tu(t):

热搜:t确定权重的方法

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  • 由题可知r(t)=h(t)*e(t)=[e-2tu(t)]*{e-t[u(t)-u(t-2)]+βδ(t-2)}。当t<2时,有r(t)=[e-2tu(t)]*[e-tu(t)]=latex.action?latex=XGludF97MH1ee3R9e-2(t-τ)e-τdτ=e-t-e-2t;当t≥2时,有
       r(t)=[e-2tu(t)]*{e-t[u(t)-u(t-2)]}+[e-2tu(t)]*[βδ(t-2)]
       =latex.action?latex=XGludF97MH1eezJ9e-2(t-τ)e-τdτ+βe-2(t-2)=e-2t(βe4+e2-1)
       即   latex.action?latex=clxsZWZ0KCB0IFxyaWdodCk9XGxlZnRce1xiZWdpbnthcnJheX17Y2N9ZV57LXR9LWVeey0ydH0g%0D%0AICAmIDDvvJx077ycMlxcZV57LTJ0fVxsZWZ0KCBcYmV0YSBlXns0fStlXnsyfS0xIFxyaWdodCkg%0D%0AICAgJiB0XGdlcSAyXGVuZHthcnJheX0%3D$由第(1)小题知,当t>2时,有
       r(t)=latex.action?latex=XGludF97MH1eezJ9e-2(t-τ)x(τ)dτ+βe-2(t-2)=e-2t[βe4+latex.action?latex=XGludF97MH1eezJ9e2τx(τ)dτ]=0
       得    β=-e-4latex.action?latex=XGludF97MH1eezJ9e2τ(τ)dτ