In Section 13.5.1, we stated that linear-phase contributions should be removed from the...

In Section 13.5.1, we stated that linear-phase contributions should be removed from the unwrapped phase curve before computation of the complex cepstrum. This problem is concerned with the effect of not removing the linear-phase component due to the factor z_r in Eq. (13.29).

Specifically, assume that the input to the characteristic system for convolution is x[n] = δ[n + r]. Show that formal application of the Fourier transform definition

The advantage of removing the linear-phase component of the phase is clear from this result, since for large r such a component would dominate the complex cepstrum.