too many combinations: Transition probability etc.

Hi

I am trying to do some statistics, but I don't know how to solve the problem 
I am working on.

I have N speech segments and I perform a 10th order LPC-analysis of each 
segment and get a 10-dimensional LPC-vector A(j)=[a1(j),a2(j),....a10(j)] 
for j=1 to N.

I then convert all A(j) to B(j)=[c1(j),c2(j),......,c10(j)] where the 
coefficients of B(j) are the LSF-coefficients corresponding to the 
LPC-vector A(j).

I want to figure out what:

- the probability of B(j) given B(j-1) is ? (transition probability)
- the probability of B(j) ?

How do I do that?

My thoughts:
The first step would be to define a discrete space S of outcomes for B(j), 
but the number of possible outcomes is very large. The coefficients of B(j) 
each
have a dynamic range from 0 to pi. If I use a discrete range from 
0,0.01,0.02,..........,3.14 that is 315 possible outcomes for any 
coefficient in B(j). Since B(j) is a 10-dimensional
vector I have 315^10 possible outcomes in the space S. That number is way 
too big to do any realistic computation in matlab......

John wrote:

> I am trying to do some statistics, but I don't know how to solve the problem
> I am working on.
>
> I have N speech segments and I perform a 10th order LPC-analysis of each
> segment and get a 10-dimensional LPC-vector A(j)=[a1(j),a2(j),....a10(j)]
> for j=1 to N.
>
> I then convert all A(j) to B(j)=[c1(j),c2(j),......,c10(j)] where the
> coefficients of B(j) are the LSF-coefficients corresponding to the
> LPC-vector A(j).
>
> I want to figure out what:
>
> - the probability of B(j) given B(j-1) is ? (transition probability)
> - the probability of B(j) ?
>
> How do I do that?

1. Calculate Pr[ B(j) | B(j-1) ].

2. Calculate Pr[ B(j) ] = sum{k = 0 to N-1} Pr[ B(j) | B(k) ]

> My thoughts:
> The first step would be to define a discrete space S of outcomes for B(j),
> but the number of possible outcomes is very large. The coefficients of B(j)
> each
> have a dynamic range from 0 to pi. If I use a discrete range from
> 0,0.01,0.02,..........,3.14 that is 315 possible outcomes for any
> coefficient in B(j). Since B(j) is a 10-dimensional
> vector I have 315^10 possible outcomes in the space S. That number is way
> too big to do any realistic computation in matlab......

Don't quantize nearly so finely and use vector quantization rather than
quantizing the individual elements.

Ciao,

Peter K.