Quantization phenomena in a class of complex biquad recursive digital filters

A special class of complex biquad recursive filters called orthogonal filters are increasingly being used in commercial TDM-FDM transmultiplexers. However, their nonlinear behavior has not been investigated to date. In a companion paper [6], we have studied the overflow phenomenon. In this paper, we examine the effects of quantization in the orthogonal filter. Stability and instability regions in the coefficient plane have been computed for the orthogonal filter operating under zero-input conditions. Theoretical upper bounds on the amplitude of limit cycle oscillations which can exist in the filter operating under both zero-input and forced-input conditions have been determined and translated to the coefficient plane. These upper bounds are compared with the maximum amplitude of forced-oscillations which have been detected in an extensive simulation. The quantization techniques considered include roundoff, magnitude, and value truncation.