Re: An idea for rough estimation of roots of a polynomial
- From: mobi <mobien@xxxxxxxxx>
- Date: Thu, 17 Jul 2008 14:58:04 -0700 (PDT)
Don't use [-A 0) for R. For R>=0, what does -R give you that R
doesn't?
You are right, it must be R>=0,where R < 1 are for zeros or roots
outside the unit circle of z-transform, and R >= 1 is for the zeros
inside or on the unit circle.
I know that there are much better methods, like the eigen values
algorithm, was just brain farting :P
~Mobien
On Jul 18, 12:28 am, dbell <bellda2...@xxxxxxx> wrote:
On Jul 17, 1:10 pm, mobi <mob...@xxxxxxxxx> wrote:
Hi all,
I have a rough idea in mind for finding the roots of a polynomial. The
approach is as follows:
1. Any Nth order polynomial can be written as: aN x^N + ... + a0,
where ai belong to set of real numbers
2. Let us introduce R (radius) terms, R^N aN x^N + R^{N-1} a{N-1}
x^{N-1}... + a0
3. Vary R in course steps bw [-A to A] and consider ai to be
coefficients of an FIR filter, pass a 0 mean, 1 variance Gaussian
noise through it.
4. Look at the Spectrum of the filtered noise, find the frequencies
where spectrum has notches.
roots are at R exp{(+/-) j*2*pi*fn/Fs}, where fn is the frequency
where the notch is.
Of course i already see several problems, how to define [-A A], steps
of R, computationally very complex etc. But i thought its interesting
to share, please feel free to criticize, suggest improvements.
~Mobien
Prohibitively expensive computationally.
But... skip the noise, don't filter anything. Treat vector [R^N aN
R^{N-1} a{N-1} ... a0] as the impulse response of the filter and FFT
the zeropadded vector.
Don't use [-A 0) for R. For R>=0, what does -R give you that R
doesn't?
Dirk
.
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