Hi I have a 10-dimensional vector v(t)=(C1(t),C2(t),......,C10(t)) where Cj(t) is between 0 and pi for any t. I let t run from t=0 to t=T and get a set S of vectors S={v(0),v(1),.....,v(T)} How do I map this set S into a discrete set D ? And how do I calculate the probability of any discrete vector in D? Thanks...

# quantization

Started by ●December 3, 2005

Reply by ●December 4, 20052005-12-04

You first need to define some distortion measure or performance measure for the mapping. Then, given the distortion measure one may design an optimal mapping. John wrote:> Hi > > I have a 10-dimensional vector v(t)=(C1(t),C2(t),......,C10(t)) where Cj(t) > is between 0 and pi for any t.OK, this is a curve in a 10 dimensional space.> I let t run from t=0 to t=T and get a set S of vectors > S={v(0),v(1),.....,v(T)}What's that a set of T+1 (quantized?) vectors (centroids?) along the above curve?> How do I map this set S into a discrete set D ?What is the definition of the discrete set D?> And how do I calculate the probability of any discrete vector in D?Exactly the same way you calculate the that probability someone would understand what you were asking...> Thanks...for what?

Reply by ●December 4, 20052005-12-04

> > > What's that a set of T+1 (quantized?) vectors (centroids?) along the above > curve?No, it's a set of observations.> > What is the definition of the discrete set D? >Well. lets just say that the range 0 to pi is mapped into the discrete range 0,0.1,0.2,........3.2

Reply by ●December 4, 20052005-12-04

"John" <joehatesspam@nospam.spamshit> wrote in message news:43921415$0$67256$157c6196@dreader2.cybercity.dk...> Hi > > I have a 10-dimensional vector v(t)=(C1(t),C2(t),......,C10(t)) where > Cj(t) is between 0 and pi for any t.***So v() and Cj() are continuous in time.> > I let t run from t=0 to t=T and get a set S of vectors > S={v(0),v(1),.....,v(T)}***So now you have sampled v(), eh? It's on a discrete set of time indices. Or are you suggesting (not so clearly) that S is an infinite set of vectors v?> > How do I map this set S into a discrete set D ?***Why is S not a discrete set? Actually it would help to define a couple of things: T is a positive integer. N=T ... which may seem trivial but helps the notation be more typical where there are N+1 elements in S: S={v(0),v(T/N),.....v(T-T/N),v(T)} The v(j) terms are all on discrete times and, thus are vectors: v(j) = (C1(j),C2(j),......,C10(j)). So the v() here are vectors of length 10 and S is a matrix that is 10 X (N+1)T no??? Fred