For what range of x do we integrate over? I'm assuming it has to be over the entire range over which the function is defined or the subrange that captures an entire repeating pattern of the function?
If that's true, do we still divide the dot product of f with the first basis function by 1/pi or should we instead divide by the range over which we integrated?
kmcrane
@lucida: The idea is that you want your basis functions to have unit length with respect to the L2 norm; I'm not sure that $1/\pi$ is the right constant here... In these examples, I think the interval length was supposed to be $[0,2\pi)$.
kmcrane
(So, seems like it should be more like $1/\sqrt{2\pi}$.)
For what range of x do we integrate over? I'm assuming it has to be over the entire range over which the function is defined or the subrange that captures an entire repeating pattern of the function?
If that's true, do we still divide the dot product of f with the first basis function by 1/pi or should we instead divide by the range over which we integrated?
@lucida: The idea is that you want your basis functions to have unit length with respect to the L2 norm; I'm not sure that $1/\pi$ is the right constant here... In these examples, I think the interval length was supposed to be $[0,2\pi)$.
(So, seems like it should be more like $1/\sqrt{2\pi}$.)
I like this explanation of Fourier Transform!