Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/22849
Title: Step response of a second-order digital filter with two's complement arithmetic
Authors: Ling, BWK
Tam, PKS
Yu, X
Keywords: Affine transformation
Autonomous response
Chaotic behavior
Second-order digital filter with two's complement arithmetic
Symbolic sequences
Issue Date: 2003
Publisher: Institute of Electrical and Electronics Engineers
Source: IEEE transactions on circuits and systems. I, Fundamental theory and applications, 2003, v. 50, no. 4, p. 510-522 How to cite?
Journal: IEEE transactions on circuits and systems. I, Fundamental theory and applications 
Abstract: It is well known that the autonomous response of a second-order digital filter with two's complement arithmetic may exhibit chaotic behaviors. In this paper, results of the step-response case are presented. Despite the presence of the overflow nonlinearity, it is found that the step-response behaviors can be related to some corresponding autonomous-response behaviors by means of an appropriate affine transformation. Based on this method, some differences between the step response and the autonomous response are explored. The effects of the filter parameter and input step size on the trajectory behaviors are presented. Some previous necessary conditions for the trajectory behaviors, initial conditions and symbolic sequences are extended and strengthened to become necessary and sufficient conditions. Based on these necessary and sufficient conditions, some counter-intuitive results are reported. For example, it is found that for some sets of filter parameter values, the system may exhibit the type I trajectory even when a large input step size is applied and overflow occurs. On the other hand, for some sets of filter parameter values, the system will not give the type I trajectory for any small input step size, no matter what the initial conditions are.
URI: http://hdl.handle.net/10397/22849
ISSN: 1057-7122
DOI: 10.1109/TCSI.2003.809814
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