While much of the algebra related to frequency sampling filters is justifiably omitted in the literature, several derivations are included here for two reasons: first to validate the equations used in Section 7.1; and second, to show the various algebraic acrobatics that may be useful in your future digital signal processing analysis efforts.
The frequency response of a comb filter is Hcomb(z) evaluated on the unit circle. We start by substituting ejω for z in Hcomb(z) from Eq. (7-2), because z = ejω defines the unit circle, giving
Factoring out the ...