# Inner product of two signals

1. Sep 6, 2011

### Jncik

1. The problem statement, all variables and given/known data
Hi

suppose

you're given two signals for example

$$x_{1}(t) = cos(3 \omega_{0} t)$$
$$x_{2}(t) = cos(7 \omega_{0} t)$$

and you want to find out the inner product
2. Relevant equations

3. The attempt at a solution

I mean, it's an integral right? But what will the boundaries be? from -oo to +oo or are we interested only in 1 period, hence from 0 to T?

Last edited: Sep 6, 2011
2. Sep 6, 2011

### mathfeel

Both signals have fundamental frequency $\omega_0$. So integration over any integer multiple of the fundamental period gives the same result.

3. Sep 7, 2011

### Jncik

so, if I took from -T to T it would be an interval 2 times larger than the interval of a period, which is correct right?

but if I integrate from 0 to T I will get a different result

do you mean by "the same result" that the answer to a question that wants an inner product can include any interval of integration no matter what the final arithmetic result will be?

$\cos a \cos b = \frac{\cos (a+b) + \cos(a-b)}{2}$