We can as H(z) • 1 1 (1 + − z−1)(1 z−1) H(z) 4 2 = 12 (1 z−1)2 − We can write as • Hinv(z) 21 (1 Hinv(z) z−1)2 1 − = = 41 (1 + z−1)(1 − 21 z−1) H(z) 14 = = The of inverse system are at and z z −12 Two poles are inside the unit circle, hence the system can be both stable and causal The zero is also inside the unit circle and the system is system phase Ex2: inverse system Find the transfer function and difference equation description of the inverse system of discrete LTI system, which describes multipath com-munication channel (two path communication channel) = + 1] y[n] x[n] ax[n − The system is is z-transform M bkz−k k=0 = H(z) Nk=0 akz−k
• We can H(z) as (1 − 1 z−1)(1 + 1 z−1) H(z) = 4 2 (1 − 12 z−1)2 • We can write Hinv(z) as Hinv(z) = 1 = (1 − 21 z−1)2 H(z) (1 − 41 z−1)(1 + 21 z−1) The of inverse system are at z = 14 and z = −12 Two poles are inside the unit circle, hence the system can be both stable and causal The zero is also inside the unit circle and the system is system Ex2: inverse system Find the transfer function and difference equation description of the inverse system of discrete LTI system, which describes multipath com-munication channel (two path communication channel) y[n] = x[n] + ax[n − 1] The system is z-transform is M bkz−k H(z) = k=0 Nk=0 akz−k phase
U8-L47_Solved-Examples-on-Causality-stability-and-Inverse-systems.docx