Conditions for overflow stability of a class of complex biquad digital filters

In digital communication networks, complex biquad recursive filters are increasingly being used in the processing of complex signals. This paper examines the stability properties of a class of complex biquad filters having different overflow nonlinearities. Two new sets of conditions have been derived to ensure asymptotic overflow stability of the complex biquad filter with respect to various admissible classes of input signals
X_{\sim c}
. The subscript
c
refers to the signal level of the complex input sequences; it is a measure of the degree of input scaling. When
c = 0
, the formulation degenerates to the zero-input stability problem. Using the new stability criteria, various regions of stability in the coefficient plane have been derived as a function of the factor
c
. The overflow nonlinearities considered include saturation, bit-by-bit inversion, zeroing, and modulo 2 arithmetic.