Time Interval x(t)·h(t-0) Output t< 0 y(1)=0 t+I 1<t< y()=(t+2)t+2-1 1t+2 (t+1) <t< =÷11= 1<t<2 y()=-(+2-3t-1) -是(t t>2 yt)=0
-1 -1 0 0 1 1 2 2
PROPERTIES AND EXAMPLES 1)Commutativity (t)*hb(t)=b()*(t) 2) (t)*8(t-to)=c(t-to) Sifting property: a(t)8(t=at 3)An integrator y(t)=/(r)dr So if input i t)=6(+) It g(t)=h(t) h(t)=/6(7)dr=u( That is ()=x(t)米h()=|m(t)*(t) ITdT 4)Step response s(t)=0(t)米h()=h()*(t)
PROPERTIES AND EXAMPLES 1) Commutativity: 2) 4) Step response: 3) An integrator: