Finite-Dimensional LT Discrete-Time Systems Applying the dtft to the difference equation and making use of the linearity and the time-invariance properties of Table 3.2 we arrive at the input-output relation in the transform-domain as he加 (e0)=∑peK(e°) k=0 k=0 where Y(e/o)and X(e/)are the dfTs of vn] and xn], respectively Copyright C 2001, S K. MitraCopyright © 2001, S. K. Mitra 3 Finite-Dimensional LTI Discrete-Time Systems • Applying the DTFT to the difference equation and making use of the linearity and the time-invariance properties of Table 3.2 we arrive at the input-output relation in the transform-domain as where and are the DTFTs of y[n] and x[n], respectively ( ) ( ) 0 0  =  −  = −   =  j M k j k k j N k j k k d e Y e p e X e ( ) j Y e ( ) j X e