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Autonomous response of a third‐order digital filter with two's complement arithmetic realized in cascade form
Author(s) -
Ling Bingo WingKuen,
Hung WaiFung,
Tam Peter KwongShun
Publication year - 2004
Publication title -
international journal of circuit theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.364
H-Index - 52
eISSN - 1097-007X
pISSN - 0098-9886
DOI - 10.1002/cta.261
Subject(s) - complement (music) , control theory (sociology) , set (abstract data type) , order (exchange) , cascade , state (computer science) , filter (signal processing) , digital filter , arithmetic , mathematics , transient response , transient (computer programming) , third order , computer science , algorithm , engineering , law , artificial intelligence , chemistry , operating system , biochemistry , control (management) , political science , computer vision , programming language , finance , chemical engineering , complementation , electrical engineering , economics , gene , phenotype
In this letter, results on the autonomous response of a third‐order digital filter with two's complement arithmetic realized as a first‐order subsystem cascaded by a second‐order subsystem are reported. The behaviour of the second‐order subsystem depends on the pole location and the initial condition of the first‐order subsystem, because the transient behaviour is affected by the first‐order subsystem and this transient response can be viewed as an excitation of the original initial state to another state. New results on the set of necessary and sufficient conditions relating the trajectory equations, the behaviours of the symbolic sequences and the sets of the initial conditions are derived. The effects of the pole location and the initial condition of first‐order subsystem on the overall system are discussed. Some interesting differences between the autonomous response of the second‐order subsystem and the response due to the exponentially decaying input are reported. Some simulation results are given to illustrate the analytical results. Copyright © 2004 John Wiley & Sons, Ltd.