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.
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.
|Divisions :||Faculty of Engineering and Physical Sciences > Mathematics|
|Date :||17 January 1997|
|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.|
|Depositing User :||Mr Adam Field|
|Date Deposited :||27 May 2010 14:40|
|Last Modified :||23 Sep 2013 18:32|
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