A Comparison of $\Delta$ Coefficients and the $\delta$ Parameterization, Part II: Signal Growth
Daniel Y. Abramovitch · 2018
The multinotch was introduced in [1] as a way to parameterize digital filters so as to preserve numerical fidelity of the filter while providing precalculation to reduce computational latency. Still, as the sample rate got large relative to the frequencies being filtered, the biquad coefficients in the multinotch got sensitive. A coefficient adjustment called Δ coefficients introduced in [2] worked extremely well on coefficient sensitivity, but did not address potential signal overflow problems. The δ parameterization [3], [4] is another method of adjusting digital filter coefficients to compensate for relatively high sample rates. A comparison of the two was made in [5]. The δ operator also is reputed to have the advantage of generating a differential form of the filter [6]. This paper will examine that, in the context of signal growth. Finally, we will propose an alternative, differential form of the biquad cascade and examine that.