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1、7-10 THE CONVOLUTION INTEGRAL,？ ？ ？,Since:,Define t=+, then dt=d, and =t, while = t=. Therefore,For t0, the input e(t)=0. r(t)=0 for t0 Such systems are said to be causal.,Since h(t)=0 for tt), so,Convolution integral 卷积,0,任意激励可以分解成一系列冲激激励之和,n，0，e*(t)e(t),Excitation：(t) Zero-state response: h(t),Tim
2、e shift: (tk) h(tk),r(t)=e(t)*h(t),If = t，then =t，d = d； =0，= t； =t，=0。,r(t)=h(t)*e(t),r(t)=e(t)*h(t)=h(t)*e(t),解：,The graphical procedure for evaluating the convolution integral,If e(t)=1(t), h(t)=et1(t),Folding: Take the mirror image of h() about the ordinate axis to obtain h().,Displacement: Shif
3、t or delay h() by t to obtain h(t).,Multiplication: Find the product of h(t) and e().,Integration: For a given time t, calculate the area under the product h(t)e() for 0t to get r(t) at t.,Overlapping region,例：,解：,0t1：,t1：,裘阿梅里积分（杜汉谟积分）,? ?,t=0，e(0) 1(t),Excitation：1(t) Zero-state response: r1(t),叠加积分，裘阿梅里积分,例：R1=R2=1，C=1F，求uC(t)的零状态响应。,解：,全响应=零输入响应+零状态响应,
