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The squared magnitude response of a linear channel, denoted by |H (f)| 2 is shown in Figure. Assume that the gap T = 1 and the noise variance s2n = 1 for all sub-channels.
(a) Derive the formulas for the optimum powers P1, P2, and P3 allocated to the three sub channels of frequency bands (0, W1), (W1, W2), and (W2, W).
(b) Given that the total transmit power P = 10, l1 = 2/3 and l2 = 1/3, calculate the corresponding values of P1, P2, and P3.
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