= + 1 H(z) az−1 The inverse system is • 1 1 Hinv(z) = = + 1 az−1 H(z) The corresponding difference equation description is • + = 1] y[n] ay[n x[n] − The inverse system is both stable and causal when |a| < 1 • Ex3: inverse system Find the transfer function of the inverse system and is the inverse sys-tem stable and causal? 5 1 7 1 n n = 2[n] + 2 ( 2 2 ( 4 ) h[n] u[n] − −
H(z) = 1 + az−1 • The inverse system is Hinv(z) = 1 = 1 H(z) + az−1 1 • The corresponding difference equation description is y[n] + ay[n − 1] = x[n] • The inverse system is both stable and causal when |a| < 1 Ex3: inverse system Find the transfer function of the inverse system and is the inverse sys-tem stable and causal? h[n] = 2[n] + 5 1 n 7 1 n ( − ( − ) u[n] 2 2 2 4
U8-L47_Solved-Examples-on-Causality-stability-and-Inverse-systems.docx