invfreqs -> invfreq and scaling

[Sergei Steshenko]

Hello,

I am trying to fit a bell-like curve (rather, a curve resembling frequency
response of oscillating loop) using 'invfreqs' function from 'signal'
package.

Under the hood the true job is done by 'invfreq' of the same package.

Conceptually the code I have looks like this:

H = <some_expression>;
[B,A] = invfreqs(H,F,4,6,W);

The 'W' vector is generated like this:

W(2:end) = (1 ./ (abs(H(2:end)) / max(abs(H(2:end)))));

, so it doesn't depend on 'H' scaling.

In my use case the leftmost point is quite critical, so I have this

W(1) = K * W(2); # K is much greater than 1
.

In order to improve quality of fitting I tried to increase 'K', but after
some 'K' value I'm getting messages like these:

"
warning: matrix singular to machine precision, rcond = 1.19893e-18
warning: attempting to find minimum norm solution
warning: matrix singular to machine precision, rcond = 1.19893e-18
warning: attempting to find minimum norm solution
",

and the quality of fitting deteriorates.

FWIW, max(abs(H)) is about 10 (i.e. about 20db).

For no good reason I've tried to replace

H = <some_expression>;

with

H = 10 * <some_expression>;
.

To my surprise the transfirmation allows me to increase 'K' 20x without 
getting the above warning and I'm getting a "perfect" fit - it now 
asymptotically behaves as it should.

I think this scaling issue/workaround is very fishy - because I am on X86,
i.e. an FPU and double precision is used, so with my 'H' values in dynamic 
range less than 60db scaling by +20db should not really matter.

Any ideas ?

Thanks,
  Sergei.

P.S. Octave version is 3.0.5, 'signal' version is 1.0.8.