# Finding the orthonormal basis for cosine function

1. Mar 10, 2015

### aiq25

1. The problem statement, all variables and given/known data
si(t) = √(((2*E)/T)*cos(2*π*fc*t + i*(π/4))) for 0≤t≤T and 0 otherwise. Where i = 1, 2, 3, 4 and fc = nc/T, for some fixed integer nc.
What is the dimensionality, N, of the space spanned by this set of signal? Find a set of orthonormal basis functions to represent this set of signals. Plot the locations of si(t) (i = 1, 2, 3, 4) in the signal space.

2. The attempt at a solution
Dimensionality N = 4.
I know how to find the orthonormal basis functions for square waves, because so far we were just given square waves. We used the Gram-Schmidt orthogonalization procedure. My question is how do I find it when the function is a sine wave?

Just looking for some directions. :)

Thank You.

2. Mar 12, 2015

### BvU

What is $\cos(\alpha + {\pi\over 4})$, what is $\cos(\alpha + {\pi\over 2})$, $\cos(\alpha + {3\pi\over 4})$ and $\cos(\alpha + \pi)$ when evaluated ?