Frequency Interpretation of z-domain transfer function

Recall that we showed the relationship between the z-transform 

Given any z-domain expression, we can generate the equivalent fi equency domain expression by simply replacing z with In section 10.2.6, we explained that the spectrum A(e ) of a digital signal is periodic with period 271 for normalised frequency. This can be thought of as a function which sweeps out a circle of radius 1 in the z-domain. The fi equency domain is in effect the particular slice on the z-domain that this circle describes. 

---