˜ = / where b bp al Then we can write as Hinv • (1 z−l N−l dkz−1) − = Hinv(z) k=1 M−p( − −1) ˜ −p 1 bz ckz k=1 The zeros of are the poles of H(z) Hinv(z) The poles of are the zeros of H(z) Hinv(z) System defined by a rational transfer function has an inverse system We need inverse systems which are both stable and causal to invert the distortions introduced by the system The inverse system is stable and causal if all poles are Hinv(z) inside the unit circle (z) Poles of are zeros of Hinv(z) Inverse system stable and causal inverse of an LTI system Hinv(z): exists all the zeros of are inside the unit circle H(z) if and only if H(z) The system with all its poles and zeros inside the unit circle is called as system minimum-phase The magnitude response is uniquely determined by the phase response and vice-Vera For a system the magnitude response is uniquely minimum-phase by the phase response and vice-versa
˜ = / where b bp al • Then we can write Hinv as z−l N−l (1 − dkz−1) Hinv(z) = k=1 ˜ −p M−p( − −1) bz k=1 1 ckz The zeros of H(z) are the poles of Hinv(z) The poles of H(z) are the zeros of Hinv(z) System defined by a rational transfer function has an inverse system We need inverse systems which are both stable and causal to invert the distortions introduced by the system The inverse system Hinv(z) is stable and causal if all poles are inside the unit circle Poles of Hinv(z) are zeros of (z) Inverse system Hinv(z): stable and causal inverse of an LTI system H(z) exists if and only if all the zeros of H(z) are inside the unit circle The system with all its poles and zeros inside the unit circle is called as minimum-phase system The magnitude response is uniquely determined by the phase response and vice-Vera For a minimum-phase system the magnitude response is uniquely by the phase response and vice-versa
U8-L47_Solved-Examples-on-Causality-stability-and-Inverse-systems.docx