In considering the implementation of homomorphic systems for convolution, we restricted...

In considering the implementation of homomorphic systems for convolution, we restricted our attention to input signals with rational z-transforms of the form of Eq. (13.32). If an input sequence x[n] has a rational z-transform but has either a negative gain constant or an amount of delay not represented by Eq. (13.32), then we can obtain a z-transform of the form of Eq. (13.32) by shifting x[n] appropriately and multiplying by −1. The complex cepstrum may then be computed using Eq. (13.33).

Suppose that x[n] = δ[n] − 2δ[n − 1], and define y[n] = αx[n − r], where α = ±1 and r is an integer. Find α and r such that Y(z) is in the form of Eq. (13.32), and then find