Chapter 10 Multirate Digital Signal Processing
Chapter 10 Multirate Digital Signal Processing
S 10.1 Basic Sample Rate Alteration Devices Time-Domain Characterization 内-2n 0,otherwise y[n]=x[nM] (10.2) u↓M yln]=x[nM]
§10.1 Basic Sample Rate Alteration Devices = ± ± = otherwise x n L n L L xu n 0, [ / ], 0, , 2 ,... [ ] (10.1) y[n] = x[nM ] (10.2) Time-Domain Characterization L xu x[n] [n]=x[n/L] M x[n] y[n]=x[nM]
Input Sequence 派 业 20 25 30 35 Time index n. Output sequence up-sampled by3 001 5 10 15 20 25 30 35 40 45 50 Time index n Input Sequence epntdu 15 20 25 30 35 40 50 Time index n Output sequence down-sampled by 3 it I Tr 20 35 50 Time index n
x[n]=xa(nT) y[n]=x(nMT) M Input sampling frequency Output sampling frequency FT=1/T F'T=1/T'=FT/M x[n]=xa(nT) 0. Input sampling frequency Output sampling frequency F=1/T F'T=1/T'=LFT
Input sampling frequency FT=1/T Output sampling frequency F’T=1/T’=LFT L = xa(nT/L), n=0,±L, ±2L,… 0, otherwise xu x[n]=x [n] a(nT) FT=1/T Input sampling frequency F’T=1/T’= FT /M Output sampling frequency M x[n]=xa(nT) y[n]=xa(nMT)
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=-o0
Frequency-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 ∞ =−∞ −