卷积练习题

iikiiikbiaikhif)()()()(第七章一、用定义求卷积和例二、图解法求卷积解：1重合面积为零:f1(t)*f2(t)=0、例：f(k)=akε(k),h(k)=bkε(k)，求yzs(k)。*0a1f1(t)tf2(t)t02b解：yzs(k)=f(k)*h(k)当i0,ε(i)=0；当ik时，ε(k-i)=0)()(0kbakykiikizs)(0kbabkiikbakbbabababkkk,)1(,111ε(k)*ε(k)=(k+1)ε(k)dtffff)()(2121计算0t10.....2tifdtffff)()(212121.....3tif1021021)(4)(2tabdtbaff)12(4tab三、用性质求卷积和f1(t)*f2(t)=(1-e–t)ε(t)–[1-e–(t-2)]ε(t-2)例1：f1(t)如图,f2(t)=e–tε(t)，求f1(t)*f2(t)32......4tifdtbafft)(21221)23(4)(421221ttabtabt0..........3......521fftif解：f1(t)*f2(t)=f1’(t)*f2(–1)(t)f1’(t)=δ(t)–δ(t–2))()e1()(e)(ded)(e)(00)1(2ttttftttt注意：当f1(t)=1，f2(t)=e–tε(t)，套用f1(t)*f2(t)=f1’(t)*f2(–1)(t)=0*f2(–1)(t)=0显然是错误的。f1(t)t201