84.1 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 ∑dkzY()=∑pk=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