Figure 1.53: Location of poles in a system minimum-phase Ex1: stable and causal system Find the transfer function of an inverse LTI system described by a dif-ference equation 1 1 − 1] + 4 2] = + 4 1] 8 2] y[n] y[n y[n x[n] x[n − − − − − Is the system stable and causal? Solution: find the from the difference equation and then z-transform find the impulse response is z-transform M bkz−k k=0 = H(z) Nk=0 akz−k 1 + z−1 z−2 − 1 1 = 4 8 H(z) 14 + 1 − z−1 z−2 Find the poles and zeros of and write in the product form H(z) •
Figure 1.53: Location of poles in a minimum-phase system Ex1: stable and causal system Find the transfer function of an inverse LTI system described by a dif-ference equation y[n] − y[n − 1] + 1 y[n − 2] = x[n] + 1 x[n − 1] − − 2] 4 4 8 Is the system stable and causal? Solution: find the z-transform from the difference equation and then find the impulse response z-transform is M bkz−k H(z) = k=0 Nk=0 akz−k 1 + 1 z−1 − 1 z−2 H(z) = 4 8 1 − z−1 + 14 z−2 • Find the poles and zeros of H(z) and write in the product form
U8-L47_Solved-Examples-on-Causality-stability-and-Inverse-systems.docx