Re: System Identification

On 30 Jun, 21:09, Vladimir Vassilevsky <antispam_bo...@[EMAIL PROTECTED]
>
wrote:
> Rune Allnor wrote:

> Here is the typical one:
>
> http://www.abvolt.com/misc/data.cpp

Greg already suggested Prony's method, and I agree with that.
I have a version lying around which was based on stationary
data (whereas your data is a transient.) My version computes
this 10'th order prediction operator:

gv = 1.0000
    0.4854
   -5.7894
    5.1015
    1.1272
   -5.1854
    4.3738
    1.5878
   -3.8126
    0.7763
    0.3344

If you plot the root locations of this polynomial
on top of the spectrum of your data,

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% d is the posted data,
% gv is the polynomial above

N=length(d);
thv=(0:N-1)/N*2*pi-pi;
clf
plot(thv,20*log10(abs(fft****ft(fft(d)))),'b')
R=roots(gv);
[rth,r]=cart2pol(real(R),imag(R));
hold on
ax=axis;
axis([-pi pi ax(3:4)])
plot([1;1]*rth',ax(3:4)'*ones(1,length(rth)),'r');
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

you can see that the roots line up pretty
well with the features in the data, if not
quite, at low frequencies.

I would go one step further and use a version of
Prony's method that work with transients. I don't
have an implementation for that right now, and
the one recipe I know of was out of print when
I hunted for it in 1994-95.

Anyway, it seems a Transient version of Prony's
method might be worth investigating.

Rune