Sinusoidal response of a second-order digital filter with two’s complement arithmetic

Ling, Wing-Kuen and Tam, Peter Kwong Shun (2003) Sinusoidal response of a second-order digital filter with two’s complement arithmetic. IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications, 50 (5). pp. 694-698. ISSN 1057-7122

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Full text URL: http://dx.doi.org/10.1109/TCSI.2003.811028

Abstract

In this paper, results of the sinusoidal response case are presented. It is found that the visual appearance of the trajectory of the sinusoidal response case is much richer than that of the autonomous and step response cases. Based on the state space technique, the state vectors to be periodic are investigated. The set of initial conditions and the necessary conditions on the filter parameters are also derived. When overflow occurs, the system is nonlinear. If the corresponding symbolic sequences are periodic, some trajectory patterns are simulated. Since the state space technique is not sufficient to efficiently derive the sets of initial conditions and the necessary conditions on the filter parameters, a frequency-domain technique is employed to figure out the set of initial conditions. When the symbolic sequences are aperiodic, an elliptical fractal pattern or random-like chaotic pattern is found.

Item Type:Article
Additional Information:(c) 2001 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.
Keywords:Sinusoidal response, chaotic behavior, second-order digital filter with two’s complement arithmetic
Subjects:H Engineering > H310 Dynamics
Divisions:College of Science > School of Engineering
ID Code:3066
Deposited By:INVALID USER
Deposited On:28 Jul 2010 14:37
Last Modified:05 Jun 2013 15:49

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