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- W1438608522 abstract "This chapter discusses autonomous response of digital filters with two's complement arithmetic. The two's complement arithmetic involves a periodic discontinuous nonlinear function, and the dynamics of digital filters could be very complicated even when no input signal is applied. Limit cycle and chaotic behaviors could occur even for second-order digital filters. The second-order real digital filters are represented by a state space model. The necessary and sufficient conditions for the nonlinear system to behave as a linear system after a number of iterations are given. It is found that once the initial conditions—the filter parameters and the input signal—are given, the state variables and the symbolic sequences can be uniquely defined by equations. It is found that the system would behave as a linear system after a number of iterations if and only if the state vector toggles between two points on a particular straight line of the phase plane. It is observed that the state vector toggles between two states in a steady state on a particular straight line. Several conditions for exhibiting eventually periodic state vector are also presented in the chapter." @default.
- W1438608522 created "2016-06-24" @default.
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- W1438608522 date "2007-01-01" @default.
- W1438608522 modified "2023-10-16" @default.
- W1438608522 title "AUTONOMOUS RESPONSE OF DIGITAL FILTERS WITH TWO'S COMPLEMENT ARITHMETIC" @default.
- W1438608522 doi "https://doi.org/10.1016/b978-012372536-3/50005-3" @default.
- W1438608522 hasPublicationYear "2007" @default.
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