I'm interested in analyzing a windowed signal in terms of a weighted sum of sawtooth waves. Being a somewhat DSP newbie, is there an obvious approach to this? I realize that sawtooth waves don't form an orthogonal basis like sinusoids do, so the problem is probably a bit ill-defined. A least squares solution or some other relaxation would probably suffice.
I could imagine constructing a matrix of sawtooth waves of different fundamental frequencies (cf. DFT/DCT matrix) but I'm not sure e.g. how phase would affect the analysis.
I could also consider low-passing + comb filtering the signal for each fundamental frequency, but constructing an array of such non over-lapping filters would seem cumbersome and inefficient.
Also doing a Fourier transform and running an analysis over all fundamentals and their harmonics would seem feasible, but clumsy.
Is there a go-to solution to a problem like this?