[sdiy] Waveform analysis into non-sine components

[Magnus Danielson]

On 04/14/2012 12:21 PM, Tom Wiltshire wrote:
> Thanks Jim.
>
> Explanations I can understand are appreciated wherever they come from.
>
> I'm still curious about these bases though. How do I know whether a basis is incomplete, complete, or overcomplete?

If you have a set of these waveforms you can reduce them to orthogonal 
waveforms by first deciding one as basis, then for the next you find the 
correlation with the first one, then remove that amount from the second 
one. Then you have two waveforms which is orthogonal to each other. Then 
you do the same to the third, but using both of the orthogonals. As you 
do this, eventually you have orthogonalized all the waveforms. Now, 
consider that you have N samples, then you need N non-zero waveforms to 
be complete. If you have less than N, you have an incomplete set and 
well, if you started with more than N and have N remaining you have 
overcomplete set.

> I've been looking into the wavelet analysis that Neil J mentioned, and it's interesting stuff, since it can be reasonably applied to transients and the attack portion of waveforms. Whilst I've tried doing fourier analysis on these, the results never really seem convincing - unsurprisingly.
> I'd like to experiment with wavelets, but I'm not clear what constitutes a basis set of wavelet functions. Obviously I can dream up some functions at different scales and use cross-correlation to see whether that function is a good fit for my waveform, but it's a bit random. Presumably there's some reason why you'd use some and not others. For example, are wavelet scales related harmonically like the sine waves in fourier analysis?

If you try to analyze the base-vectors from one transform in another, 
they will not make much sense usually. This only shows that the 
transforms are different. It's thus expected.

Do you know what a phasor are?

Cheers,
Magnus