Unit delay operator as parameter in function I'm busy trying to implement a filter from this paper. I'm a bit confused with one particular step (30e in the paper). 

Basically I need to find the zero frequency gain (K) of the following whitening/comb filter:



The relevant steps in the algorithm are:



and



where $q^{-1}$ is the unit delay operator, $\omega_0$ is the fundamental freq of the comb and $\rho$ is a constant.

I'm not sure how to calculate K. Since the function isn't acting on anything, what should be delayed? The signal (at time t)? Or does passing a constant in place of the delay mean it should be replaced?

Any help is greatly appreciated!

EDIT

Some clarification on $q^{-1}$: 


  The right-shift operator $q^{-1}$ acts on a discrete-time signal f(k, T) as $q^{-1}$ f(k, T) = (k − 1, T). The operation $q^{-1}$ therefore shifts the discrete-time signal to the right by one sampling interval.
With $A(q^{-1},t)$ as given in the formula you get

$$A(1,t)=\prod_{k=1}^n(1-2\cos(k\hat\omega_0(t))+1)\tag{1}$$

and

$$A(\rho,t)=\prod_{k=1}^n(1-2\cos(k\hat\omega_0(t))\rho+\rho^2)\tag{2}$$

So $K(t)$ is simply the quotient of (1) and (2).