Example:find the output of the system H(z)= b+b2 I-az-T a,with input x[n]. Solution1: hin]=ha"uln]+ba"-uln-I] IIR Impulse Response 长度无限 yIri]=x[n]*hr]=x[k]hn-k] even if we only wanted to compute the output over a finite interval.it would not be efficient h n-k Illustration for the IIR case by convolutionwith input x[n]. even if we only wanted to compute the output over a finite interval, it would not be efficient to do so by discrete convolution, since the amount of computation required to compute y[n] would grow with n . 5 1 0 1 1 ( ) , | | | |, 1 b bz H z z a az − − + =  −       1 0 1 1 n n h n b a u n ba u n − = + −           n k y n x n h n x k h n k =− =  = −  Illustration for the IIR case by convolution IIR Impulse Response 长度无限 Example: find the output of the system Solution1: