The Fourier Series of a function $y(x)$ is its expansion into sines and cosines:
$$y(x)= a_0+a_1\cos(x) +b_1\sin(x)+a_2\cos(2x)+b_2\sin(2x)+…$$
An Orthogonal Basis for an inner product space $V$ is a basis for $V$ whose vectors are mutually orthogonal.
For the Fourier Series example above, how do I correctly specify the orthogonal basis $B$ ?
Is it simply $B=\{\cos(x),\sin(x),\cos(2x), \sin(2x),\dots\}$?
Best Answer
Yes, together with the constant function.