The multinotch, part II: Extra precision via Δ coefficients

In [1], we presented a new digital filter architecture, the multinotch, which minimized the computational latency while preserving numerical accuracy even in the presence of severe quantization. While this method is far more accurate than discretizing polynomial filters, it can still be susceptible to problems caused by a sample rate which is significantly higher than the frequencies of the features that the filter is trying to implement. This paper presents a modification, called Δ coefficients, which preserve all the positive properties of the multinotch while dramatically increasing the numerical accuracy over a large frequency range.