# Parseval's Theorem - Average Power of the difference of functions

• Engineering

## Homework Statement:

Given a function $e(t) = f(t) - g(t)$, find the average power of the function.

## Relevant Equations:

Parseval's theorem
Hi,

So I have a quick conceptual question about Parseval's theorem in this application. In previous parts of this question, we have found the average powers of both $f(t)$ and $g(t)$ by integration and using the complex Fourier series respectively (not sure if this is relevant to my question). I wanted to know how do we use these to calculate the average power of e(t)?

The answer simply does subtract the two aforementioned expressions to get the answer. However, I was wondering why we wouldn't need to consider the 'cross-terms'? So in the average power integral, we are dealing with $|e(t)|^2 = |e(t)||e^*(t)| = |f(t) - g(t)||g^*(t) - f^*(t)|$ and wouldn't this contain terms that look like $f(t) g^*(t)$ and $f^*(t) g(t)$ (omitting the signs for now)? The calculation that they have done does not include any of these and I was wondering whether we are allowed to combine average powers like that?