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1. Use the recursive equations (8.18) to verify the expressions (8.19) of theorem 86 for r=1,2,3 Equations (8.17) lead to the following Fourier transform relations: p(21) (w) = 2-1/2H, (w/2) PG) (w/2), (8.18a) Q(25) (W) = 2-1/2H1 (w/2) PG) (w/2), (8.18b) p(2j+1)(W) = 2-1/2H, (w/2) Q6w/2), (8.180) Q(2j+1)(w) = 2-1/2 H1 (w/2) Q0) (w/2). (8.180) The above recursions, in the frequency domain, have a simple closed form solution found by inspection and shown in the following theorem. Theorem 36. Let (b.3-1 - Bibo] denote the binary representation of the superscript r, i.e., r = b)-123-1+...+6020, and the bits ok, 0