Wiley signals and systems e book TLFe BO 359

344 14 Discrete-Time EI'I-Svstenis Figure 14.5: System function H ( z ) of a, discrete Ill'l-bystern The system finirtion H ( z ) (with it®ion of convcrgmcc) is il completc dcscription of the input output behaviour of a discrete LTI-system It makes it possible to give the output sequcncc y[k] for any given input sequence xc[k] nctions from rence Equations A systclrn fiinrtion can easily bc found from a difference equation using thc shift theorem of the z-tiarisforni (see Table 13.1) N7e will demonstrate the prowdure with a few examples Example 14.1 A discrete delay circuit delays the input signal Its 'difference cquation is y[k] = IC[k - 11 Using thc z-transform and its shift tfieorcrn (Table 13.1 ) with (14.18) /.; = yields Y ( z j = Z(y[X-J)= Z{.C[k - 11) = z - ' X ( z ) (14.19) -4 comparison with (14.17) givcs the system func*tionof the discrete delay circuit (see Figurc 14.6) H(x)= - I Figure 14.6: System €imct.ionof the discrete delay circiiit