[AmishDude]

Well, the problem is that engineers got a hold of the beauty of the Fourier series and then abuse you with it. Stand back. Consider the vector space of real-to-real functions. The cardinality of this set is of a higher "level of infinity" than that of the reals. Yet, it has a countable basis. Moreover each member of the basis is periodic. Moreover, the basis is easily-describable. Absolutely gorgeous idea.

[weikel]

Just a summation of some UGLY trignometric integrals to me.