Finite-Dimensional LT Discrete-Time Systems Applying the z-transform to both sides of the difference equation and making use of the linearity and the time-invariance roperties of Table 3. 9 we arrive at N M ∑dkzY(=)=∑PkzX(=) k=0 k=0 where Y(z) and X(z)denote the z-transforms of yn] and xn] with associated RoCs, respectivel Copyright C 2001, S K MitraCopyright © 2001, S. K. Mitra 5 Finite-Dimensional LTI Discrete-Time Systems • Applying the z-transform to both sides of the difference equation and making use of the linearity and the time-invariance properties of Table 3.9 we arrive at where Y(z) and X(z) denote the z-transforms of y[n] and x[n] with associated ROCs, respectively d z Y(z) p z X(z) M k k k N k k  k  = − = − = 0 0