Hello,
I'm integrating knowledge I developped a few years ago about invfreq.m.
I'm intending to modify it in a number of ways:
- allow for the ability to specify number of zeros as s/z = 0 at the
numerator
- the current implementation is based upon zeroing
B(s)-A(s)H(s)
which can be achieved if
[1 s s^2 ... s.H(s) s^2H(s)][B; A(2:nA)] = H(s)
as the independant term of A is normalised to 1. This results in a
complex equation system in real coefficients:
L(s) X = H(s)
Real results are obtained by multiplying both sides by conj(L(s)). On
paper, this is fine, but the net result is to square the condition number
of the original system. As a result, computing filters with around 10
coefficients quickly leads to badly conditionned matrices.
I implemented two work-arounds:
1) add an option to scale the frequencies by the maximum of them. The
coefficients are to be unscaled accordingly afterwards
2) Split the orginal system as
[real(L(s)); imag(L(s))][B; A(2:nA)] = [real(H(s)); imag(H(s))]
This avoids the squaring of the condition number in the first place
- Furthermore, the noise structure on [L(s) H(s)] is specific: the first
nB+1 columns are unnoised, the rest is noised. So I added the ability to
solve the system by three methods:
-Least Square, using usual left division
-Total Least Square, under the hypothesis that all columns are
contaminated by the same amount of noise
-Mixed Least Square, where the noised part is solved using TLS, and the
unnoised part using back-susbtitution
- The actual function also returns a noise estimate
That's a lot of changes. I would like to have those changes reviewed
instead of pushing them directly. Who volunteers to have a look at them ?
Pascal
Save money, use Scarlet Internet solutions: as from EUR 25/month... visit
http://www.scarlet.be/
------------------------------------------------------------------------------
Beautiful is writing same markup. Internet Explorer 9 supports
standards for HTML5, CSS3, SVG 1.1, ECMAScript5, and DOM L2 & L3.
Spend less time writing and rewriting code and more time creating great
experiences on the web. Be a part of the beta today.
http://p.sf.net/sfu/beautyoftheweb
_______________________________________________
Octave-dev mailing list
[email protected]
https://lists.sourceforge.net/lists/listinfo/octave-dev
