Occurrence of elliptical fractal patterns in multi-bit bandpass sigma delta modulators

Ho, C, Ling, B, Reiss, J and Yu, X 2005, 'Occurrence of elliptical fractal patterns in multi-bit bandpass sigma delta modulators', International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 15, pp. 3377-3380.


Document type: Journal Article
Collection: Journal Articles

Title Occurrence of elliptical fractal patterns in multi-bit bandpass sigma delta modulators
Author(s) Ho, C
Ling, B
Reiss, J
Yu, X
Year 2005
Journal name International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Volume number 15
Start page 3377
End page 3380
Total pages 4
Publisher World Scientific Publishing
Abstract It has been established that the class of bandpass sigma delta modulators (SDMs) with single bit quantizers could exhibit state space dynamics represented by elliptic or fractal patterns confined within trapezoidal regions. In this letter, we find that elliptical fractal patterns may also occur in bandpass SDMs with multibit quantizers, even for the case when the saturation regions of the multibit quantizers are not activated and a large number of bits are used for the implementation of the quantizers. Moreover, the fractal pattern may occur for low bit quantizers, and the visual appearance of the phase portraits between the infinite state machine and the finite state machine with high bit quantizers is different. These phenomena are different from those previously reported for the digital filter with two's complement arithmetic. Furthermore, some interesting phenomena are found. A bit change of the quantizer can result in a dramatic change in the fractal patterns. When the trajectories of the corresponding linear systems converge to a fixed point, the regions of the elliptical fractal patterns diminish in size as the number of bits of the quantizers increases.
Subject Calculus of Variations, Systems Theory and Control Theory
Keyword(s) Bandpass sigma delta modulator
multibit
fractal behaviors
DOI - identifier 10.1142/S0218127405013976
Copyright notice © World Scientific Publishing Company
ISSN 0218-1274
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