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
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