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Question - Recall the Power function:
Power(ωk) = (t=1ΣnXtcos(2 πωkt))2 + (t=1Σn Xt sin(2πωkt))2
Show that the power measures the squared correlation between the data X = (Xt, t = 1,..., n)' and the sinusoidal. That is, show that Power (ωk) = Ak · ρ^2 (X, Uk) + Bk · ρ^2 (X, Vk) where Uk = (cos(2 πωkt), t = 1, . . . , n)' and Vk = (sin(2 πωkt) t = 1,...,n)' , and p^(X, Y) is the sample correlation between the n-dim vectors X and Y. Also, what are Ak and Bk?
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