Autonomous Response of Digital Filters with Two’s Complement Arithmetic
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چکیده
In a real situation, digital filters are usually implemented via the two’s complement arithmetic because subtraction can be implemented easily via addition. However, 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. In this chapter autonomous response of second order lowpass and highpass digital filters associated with two’s complement arithmetic is discussed. In particular, the lowpass filter containing a DC pole and the highpass filter containing a pole located at z=−1 are discussed. Finally, various conditions for the occurrence of limit cycle and chaotic behaviors are given.
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