Husheng Li, UTK-EECS, Fall 2012

 The principle value of the phase response will exhibit discontinuities when viewed as a function of w.  We use ARG as the wrapped phase and arg as the continuous phase.

 The condition of stability is equivalent to the condition that the ROC of H(z) includes the unit circle.  If the system is causal, the impulse response h(n) must be right-sided sequence.  Causality and stability are not necessarily compatible requirements.

 For a system with system function H(z), its inverse system has function 1/H(z).  In the inverse system, the poles and zeros will be swapped.  There are two classes of LTIs:  At least one nonzero pole (IIR)  No poles (FIR)  Midterm: Oct.16, 2012  Homework: 5.1, 5.2, 5.3

 A system for which the frequency-response magnitude is a constant, referred to as an all-pass system, passes all of the frequency components of its input with constant gain or attenuation.

 If the system is stable and causal, the poles must be inside the unite circle, but no restrictions are put for the zeros.  For certain classes of problems, it is useful to impose an additional restriction that the inverse system also be stable and causal. Such systems are referred to as minimum-phase systems.  Properties:  Minimum phase-lag property  Minimum group-delay property  Minimum energy-delay property