I have many signals where each signal has a different waveform f(x). One example of such a waveform could be this f(x) sampled at 11 x positions:
I am looking for a basis, Bi, for a series expansion of f(x): $\ f(x) \simeq \sum\limits_{i=0}^m c_i B_i(x) $
The expansion should have the following properties:
- Give a good approximation with few terms (low m): low square error.
2. Given a expansion for one waveform with the following coefficient vector: $ \mathbf{c}_i $; another waveform that is "similar" to the first waveform should have nearly the same coefficient vector. By similar I mean e.g. same shape as the first but slightly wider, same shape as the first but slightly higher peak etc. The basis should NOT be scale invariant; e.g. a similar waveform but much smaller should get a very different coefficient vector.
The expansion will be used on all signals to automatically classify them into clusters; signals that have close coefficients vector belong to one cluster.
Thanks in advance for any answers!