Considering down-sampler Y(z)=∑x[Mm]z” n=-00 Let Then, 00 00 Y(e)=∑x[M例]z"=∑xn[Mim]z" n=-o0 00 = xt[k]z/M=Xn(zM) k=-00Considering down-sampler = ∑ ∞ =−∞ − n n Y(z) x[Mn]z Let Then, = ∑ = ∑ ∞ =−∞ − ∞ =−∞ − n n n n Y(z) x[Mn]z x [Mn]z int [ ] ( ) 1/ int / int M k k M = ∑ x k z = X z ∞ =−∞ −       x [ n ] = int x[n], n=0, ±M, ±2M,… 0, otherwise