Low roundoff noise augmented realizations of IIR filters

The scaling factor in a direct form II infinite impulse response (IIR) digital filter depends on only the system poles, not its zeros. Adding pole-zero cancellation pairs changes the scaling factor and the associated roundoff noise without affecting the transfer function. It is shown that with l₂ scaling, the upper bound of the noise reduction for direct form II IIR digital filters using K pole-zero cancellation pairs is about 6K dB. The authors consider parallel form 3P to be the basic structure, in which each subfilter is augmented with one or two pole-zero cancellation pairs and realized in direct form II. They seek an iterative optimization process for each subfilter to find the optimal pole-zero cancellation pairs that minimize the roundoff noise. Experimental results indicate the global optimal solution for these augmented subfilters can be obtained by using simple criteria to determine the starting points of the iterative processes. Alternative structures, illustrative examples, and overflow limit cycles are examined