# Parseval's theorem

Parseval’s theorem

This is a pretty useful theorem in signal processing field as well as in courses related with random processes. Sometimes a signal or a random process in time domain is hard to calculate, thus we want to transform it into transformation domain(e.g. frequency domain, z domain, etc.) to facilitate math. In Oppenheim’s *Signals, Systems & Inference* and Therrien’s *random process* we talked about some random processes in time domain which were sent pass through a linear system, and we need to calculate some features of output signal regarding the input signal, or vice versa.

For the energy or power of a certain signal, we might take advantage of Parseval’s theorem, since it yields some insights of how we understand the power of a signal in different domains. However, sometimes it need a little deduction to figure it out. Hereby I paste my primary dedction of it.

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