Rayleigh's identity is listed below:
) 2 / 2 1 1 \
/ |f(k)| = int||f(t)| , t = - - T .. - T|
----- \ 2 2 /
k = -infinity
sum(abs(f(k))^2, k = -infinity .. infinity) = int(abs(f(t))^2, t = -(1/2)*T .. (1/2)*T);
This identity is an extension from Parseval's theorem for the case where the function of interest is periodic. The link below provides a worksheet that confirms for a finite series that Rayleigh's identity is valid to within so many significant figures as the frequency parameter, k, increases for CASE 1. However, for CASE 2 concurrence between the integral and the finite series is not that great. I suspect I have an error somewhere that is causing the discrepancy. I thought it might be useful if I get other sets of eyes on this to help isolate the discrepancy. How I came up with Ck for CASE 2 I can create another worksheet with that derivation if requested.
Appreciate any useful feedback