Frequency-Domain Characterization x[n/2],n=0,+2,+4,… 5.0 0,otherwise ● 00 Xu(z)=∑x[n]z"=∑x[n/2]z" n=-o0 n=-00 n,even X(z)=∑x[m]z2m=X(z2) m=-00 For the factor-of-L up-sampler, Xu(z)=∑x[m]zm=X(z) m=-o0Frequency-Domain Characterization       = ± ± = otherwise x n n xu n 0, [ / 2], 0, 2, 4,... [ ] = ∑ ∞ =−∞ − n n u u X (z) x [n]z = ∑ ∞ =−∞ − n even n n x n z , [ / 2] ( ) [ ] ( ) 2 2 X z x m z X z m m u = ∑ = ∞ =−∞ − For the factor-of-L up-sampler, ( ) [ ] ( ) L m Lm u X z = ∑ x m z = X z ∞ =−∞ −