Totally of the cuff: I believe you can recast the Sims in the discrete Fourier transform as integrals of step functions. So it should work. However the width of

Totally of the cuff: I believe you can recast the Sims in the discrete Fourier transform as integrals of step functions. So it should work. However the width of the steps in the discrete dirtier transform is fixed for each n. So you'll need to be a bit clever to make sure your steps line up right of you want to build up a single infinite basis. And I would be a bit afraid that the need for things to line up would end up losing some needed span... So at least the are done things which need to be checked. The sin and cos basis is very convenient. Even more convenient is the e^(i.n.t) basis...