Inner product

Inner Product

We will use the notation $<a|b>$ to indicate the inner prodoct of $a$ with $b$ is being taken.

If we have two functions, say $x(t)$ and $y(t)$, then $<x(t)|y(t)>=\underset{a}{\overset{b}{\int }}x(t{)}^{*}y(t)dt$

Note: the $*$ indicates that we are taking the complex conjugate of $x(t)$. We could just as easily have taken the complex conjugate of $y(t)$, but it is usually displayed as shown above, as a matter of tradition.