quantization

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...

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?

>
>
> 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

"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