Fourier Transform Parseval's Theorem

Cuthbert Nyack

If the signal is assumed to be a voltage and it is applied across a 1 ohm resistor, then the ENERGY dissipated in the resistor is given by the left hand side of the equation below. Parseval's theorem states that this is also equal to integral of the square of the spectrum on the right.

Parseval's theorem is similar to the expression below for periodic signals. Since the periodic signal goes from -inf to +inf the the energy dissipated is infinite. To get a finite result, an average must be taken resulting in a POWER relationship.

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