YyW 2n J o 2n JfcB 2n J

yy V

2g2i b

2G2l B

° y = Ryy (0) = ^^ 8.2-30 Wu shows VAR{z} = ctz2 = Rzz(0) to be a 2 = Rzz (0) = jjfi2 * yy (ffl)dffl = [12Q2 + 1 8.2-31

Thus, the higher the filter Q, the better, because it is desired that ctz ^ x, so that the Rxz(t) bias term in Equation 8.2-24 for |(t) will ^ 0.

Finally, the theoretical cross-correlation function, Rxy(x) for the IBPF is examined. Wu shows this to be

1 r 2GlB

Rxy(t) = — I oxx(ca)H(jœ)ejm dœ =-^ sinc(BT/rc) cosjcot) 8.2-32

Compare this expression for Rxy(x) with the inverse Fourier transform of the IBPF, h(t):

h(t) = — I H((ra)ejraTdra = — I ejraTdra + — I ejraTdra 8.2-33

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