DECOUPLING OF THE OVERFLOW AND QUANTIZATION PHENOMENA IN ORTHOGONAL BIQUAD RECURSIVE DIGITAL-FILTERS

In this paper we examine the zero-input stability properties of the actual orthogonal filter having both overflow and quantization nonlinearities. The overflow nonlinearities considered include saturation, bit-by-bit inversion, zeroing, and modulo 2 arithmetic. The quantization techniques used may be roundoff, magnitude, or value truncation. An example demonstrates the adverse coupling effect between the overflow and quantization nonlinearities. Two criteria are therefore derived to ensure asymptotic overflow-stability of the filter in the presence of quantization. These criteria have been translated to the coefficient plane; various regions corresponding to different minimum wordlengths required to ensure decoupling of the overflow and quantization phenomena have been derived.