[jqgatsby]

so, uh, you gonna tell us the insight?

[msla]

Maybe that it's "just" a change of basis, onto a basis made of orthogonal periodic functions.

[franknstein]

Change of bases being done with orthogonal projection derived from defining scalar product of two functions via finite integral of product of two functions: f dot g = integral f(x)g(x)dx over some interval.