528 Appendix A Solutiorii to the Exercisrs Solution 14.2 a) shift-vasiaiit, because S { S [ k - :V]}= x[2(k- N)]# y[k - N] s [ k - N] : b) likewise shihvariant, see a,) C) 'L'lir systciii sets to zero every sample with odd k : Exaiuplc for N = 2: shift-rnvar.iarit The syst,rni is iiivariailt, whcn shift,ed by an even iiiirriber of cyclcs, 11ut shifting: x [ k ]by an odd niimber of cycles does iiol deliver a shifted vrrsiori of' ;q[k] Note: Systcms t h a t , a,re invariant for a cert,ain shift m d its multiples are called perzod,ic ,sii:i~fl-ziivnrznn.t Solution 14.3 a ) lJ[-1] = y'O] = Y[O] = U [ I j = L [ ] 2y[k - 11 = - ' = -2 y[2; = x[2] 2y[k - I] - ?/[A, - = (-2) - = - - "I -