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

By Charlotte Yuk-Fan Ho, Bingo Wing-Kuen Ling, Joshua D Reiss and Xinghuo Yu


It has been established that the class of bandpass sigma delta modulators (SDMs) with single\ud bit quantizers could exhibit state space dynamics represented by elliptic or fractal patterns\ud confined within trapezoidal regions. In this letter, we find that elliptical fractal patterns may\ud also occur in bandpass SDMs with multibit quantizers, even for the case when the saturation\ud regions of the multibit quantizers are not activated and a large number of bits are used for the\ud implementation of the quantizers. Moreover, the fractal pattern may occur for low bit quantizers,\ud and the visual appearance of the phase portraits between the infinite state machine and the finite\ud state machine with high bit quantizers is different. These phenomena are different from those\ud previously reported for the digital filter with two’s complement arithmetic. Furthermore, some\ud interesting phenomena are found. A bit change of the quantizer can result in a dramatic change\ud in the fractal patterns. When the trajectories of the corresponding linear systems converge to a\ud fixed point, the regions of the elliptical fractal patterns diminish in size as the number of bits\ud of the quantizers increases

Topics: H310 Dynamics
Publisher: World Scientific Publishing
Year: 2005
DOI identifier: 10.1142/S0218127405013976
OAI identifier:

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