This document discusses two methods for inverse z-transforms: the convolution method and the residue method. The residue method can be used when the function is rational in the form of p/q, with unique finite poles. It involves contour integration around the origin, inside the region of convergence. The poles are the roots of the denominator polynomial. The convolution method uses the property that the inverse z-transform of two signals multiplied in the z-domain is the convolution of their inverse z-transforms.