84.1 LTI Discrete-Time Systems in the Transform domain difference equation and making use or the e Applying the z-transform to both sides of the linearity and the time-invariance properties we arrive at ∑dkz-(z)=∑ PkE X() k=0 k=0 where y(z and x(z denote the z-transforms of yIn and xn with associated ROCs, respectively§4.1 LTI Discrete-Time Systems in the Transform Domain • Applying the z-transform to both sides of the difference equation and making use of the linearity and the time-invariance properties we arrive at d z Y(z) p z X(z) M k k k N k k  k  = − = − = 0 0 where Y(z) and X(z) denote the z-transforms of y[n] and x[n] with associated ROCs, respectively