On 1/8/12, Miller Puckette msp@ucsd.edu wrote:
Hi all --
Peter Brinkmann and Michael Goggins did some related work recently:
http://nettoyeur.noisepages.com/2010/10/doppler-effects-without-equations/
but back in the dark ages Barry Vercoe made a Music 11 ugen called 'pipadv' that added a signal into a delay line assuming the write location was continuous and could be stably differentiated (so that for each point of the delay line you could associate a fractional pposition in the incoming signal. He then interpolated to get fractional-indexed values of the incoming signal to correspond with successive sample locations in the delay line, turning the problem around backward.)
I've thought about this for a few hours but so far my only conclusion is that it's very interesting :)
Miller
The problems that I see are with orthogonality and reconstruction. A sample really just represents a sync that's centered on a point in time (in the easy case). Integer numbers of samples are orthogonal... but the fractionally-centered sample is not orthogonal to samples at all the integer indexes.
Then, the reconstruction problem follows from it. When you want to read a value from a table, does it exactly retrieve the value that was recorded there? It seems like the interpolator needs to be modified continuously with the spacing of adjacent samples.
All I know right now is, I can't spend my whole vacation on a math problem, even if it's good :)
Chuck