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

Ho, Charlotte Yuk-Fan and Ling, Bingo Wing-Kuen and Reiss, Joshua D and Yu, Xinghuo (2005) Occurence of elliptical fractal patterns in multi-bit bandpass sigma delta modulators. International Journal of Bifurcation and Chaos, 15 (10). pp. 3377-3380. ISSN UNSPECIFIED

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Full text URL: http://dx.doi.org/10.1142/S0218127405013976

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.

Item Type:Article
Additional Information: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.
Keywords:Bandpass sigma delta modulator, multi-bit, fractal behaviors
Subjects:H Engineering > H310 Dynamics
Divisions:College of Science > School of Engineering
ID Code:2709
Deposited By: Rosaline Smith
Deposited On:23 Jun 2010 14:22
Last Modified:13 Mar 2013 08:39

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