There are probably many rules. If simply making them unique (1-1) was
the problem then consider sorting the roots by increasing magnitude,
then when encountering the same magnitude, use increasing angle. That
would be 1-1. But it sounds like you may have another problem in that
a little perturbation of the roots could then change the order. So you
need a sorting method that is insensitive to small changes. You might
want to look at [first reflection coef, 2nd reflection coef, ...] since
this has the order predetermined. Intuitively (based on whatever) I am
guessing the RC values are less sensitive to small perturbations (may
be more so for certain coefs). Check the literature.
FWIW,
Dirk
Reply by John●November 28, 20052005-11-28
Hi there...
I am going to implement a Hidden Markov Model and as far as I can see it's
important
that I train the model with vectors that are unique, right?
In my case the observation vector is a 10-dimensional complex vector. The
entries in
this vector are the roots of the polynomial A(z).
As you can see - using the roots - means that the vector is _not_ unique
unless I:
a) split the vector up in 5 2-dimensional vectors and plot them and then use
the
generated pattern as a "state"
or
b) am able to ensure that there is a one-to-one mapping between the
coefficient
vector and the 10-dimensional complex vector by using some sort-rule
Which sort rule do you propose?
Thanks
------------
> Why do you want to?
>
> Dirk
>
Reply by dbell●November 28, 20052005-11-28
Is it possible? Easily. Make a sorting rule that sorts the results
based on number characteristics so that the sort is unambiguous. Use
the resulting sorted vector.
Why do you want to?
Dirk
Reply by John●November 27, 20052005-11-27
Hi
If I have a polynomial A(z)=1+a1*z^(-1)+a2*z^(-2)+.....+a10*z^(-10) and I
solve A(z)=0 and write the solution as a vector [r1,r2,....,r10] then I can
say that the action of finding the roots is a one-to-many transformation
from the coefficient vector [a1,a2,.....,a10] to the root vector
[r1,r2,...,r10]....
Is it possible somehow to ensure that the above transformation of a given
coefficient-vector always results in the same root vector ?
For example:
The above transformation of a coefficient vector a=[1,0.5,-0.25] will result
in the root vector [-0.8090,0.3090]
But [0.3090,-0.8090] is also a solution.....so is it possible somehow to
solve this problem and ensure a one-to-one mapping ??
If not, how should/could I go about it then?
Thank you .