Question

5. Let f(x) be periodic with fundamental period p and suppose that fand fare piecewise continuous on - p/2, p/2] (1) Show that I, 5(x?dx=a* + Ele? +6£) = Ele| This is Parseval's identity with the left hand side showing the "averaged" magnitude of f(x) over the interval (2) If f(x) is velocity, we can view that the sum of all coefficient squared as a measure of 'kinetic energy'; likewise, if f(x) represents displacement, we may view the sum of coefficients as some stored energy. Think of one application.

Answer 1

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