Reading notes: Discrete-time signal processing: Frequency response of rational system functions

1. The frequency of the individual 0 points corresponds

A single 0 point corresponding to a fraction of 1-az-1,a can be a complex number. When z is in the value of the unit circle, we can write this fraction as 1-rejθe-jω to analyze.

2. Multiple poles

If the system's H[n] is a real number, then the frequency response of the system must have a conjugate symmetric 0 points or poles (the system frequency response is a real coefficient polynomial). For example, assuming that the system function has a pole rejθ, then there is bound to be a conjugate pole re-jθ, so the system function of such a rational function system must exist the denominator (1-rejθz-1) (1-re-jθz-1) =1-2rcosθz-1+r2z-2.

Reading notes: Discrete-time signal processing: Frequency response of rational system functions