University of Surrey

Test tubes in the lab Research in the ATI Dance Research

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.

[img]
Preview
PDF
fulltext.pdf

Download (414kB)

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
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
AuthorsEmail
Ashwin, PeterUNSPECIFIED
Chambers, W. G.UNSPECIFIED
Petkov, G.UNSPECIFIED
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
URI: http://epubs.surrey.ac.uk/id/eprint/1386

Actions (login required)

View Item View Item

Downloads

Downloads per month over past year


Information about this web site

© The University of Surrey, Guildford, Surrey, GU2 7XH, United Kingdom.
+44 (0)1483 300800