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Lossless Digital Filter Overflow Oscillations; Approximation of Invariant Fractals

Ashwin, Peter, Chambers, W. G. and Petkov, G. (1997) Lossless Digital Filter Overflow Oscillations; Approximation of Invariant Fractals International Journal of Bifurcation and Chaos, 7. pp. 2603-2610.

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Abstract

We investigate second order lossless digital filters with two's complement overflow. We numerically approximate the fractal set D of points that iterate arbitrarily close to the discontinuity. For the case of eigenvalues of the associated linear map of the form eiθ with θ/π ∉ Q we present evidence that D has positive two dimensional Lebesgue measure. For θ/π ∈ Q we confirm that D has Lebesgue measure zero. As a by-product we get estimates of the exterior dimension of D. These results imply that if such filters are realized using finite-precision arithmetic then they will have a sizeable fraction of orbits that are periodic with high period overflows.

Item Type: Article
Additional Information: Published in International Journal of Bifurcation and Chaos, 7, 2603-2610. © 1997 World Scientific Publihsing Company. Click Click here to access the journal website.
Divisions: Faculty of Engineering and Physical Sciences > Mathematics
Depositing User: Mr Adam Field
Date Deposited: 27 May 2010 14:40
Last Modified: 23 Sep 2013 18:32
URI: http://epubs.surrey.ac.uk/id/eprint/1386

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