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Message |
John
Guest
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 Posted:
Sun Dec 04, 2005 1:15 am Post subject:
quantization |
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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... |
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NS
Guest
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| Posted:
Sun Dec 04, 2005 9:15 am Post subject:
Re: quantization |
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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:
| Quote: | 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.
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OK, this is a curve in a 10 dimensional space.
| Quote: | I let t run from t=0 to t=T and get a set S of vectors
S={v(0),v(1),.....,v(T)}
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What's that a set of T+1 (quantized?) vectors (centroids?) along the
above curve?
| Quote: | How do I map this set S into a discrete set D ?
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What is the definition of the discrete set D?
| Quote: | And how do I calculate the probability of any discrete vector in D?
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Exactly the same way you calculate the that probability someone would
understand what you were asking...
| Quote: | Thanks...
for what? |
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John
Guest
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| Posted:
Sun Dec 04, 2005 5:15 pm Post subject:
Re: quantization |
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| Quote: |
What's that a set of T+1 (quantized?) vectors (centroids?) along the above
curve?
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No, it's a set of observations.
| Quote: |
What is the definition of the discrete set D?
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Well. lets just say that the range 0 to pi is mapped into the discrete range
0,0.1,0.2,........3.2 |
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Fred Marshall
Guest
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| Posted:
Mon Dec 05, 2005 1:15 am Post subject:
Re: quantization |
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"John" <joehatesspam@nospam.spamshit> wrote in message
news:43921415$0$67256$157c6196@dreader2.cybercity.dk...
| Quote: | 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.
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***So v() and Cj() are continuous in time.
| Quote: |
I let t run from t=0 to t=T and get a set S of vectors
S={v(0),v(1),.....,v(T)}
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***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?
| Quote: |
How do I map this set S into a discrete set D ?
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***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 |
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