Variable biquadratic digital filter section with simultaneous tuning of the pole and zero frequencies by a single parameter

A new variable multi-output digital biquadratic filter section (BQ3), realizing all possible second-order transfer functions and permitting an independent tuning of the pole- and zero-frequencies and the pole-quality factor, is developed in this work. Each of the magnitude parameters is tuned by trimming of a single multiplier coefficient and for narrow-band realizations it is even possible to tune simultaneously the two frequencies by a single multiplier. The limits and the quality of this simultaneous tuning are investigated and then the sensitivities of BQ3 and the other known sections (BQ1 and BQ2) are comparatively studied. It is shown that BQ3 has a very low sensitivity for poles near z=1, ensuring thus a very high accuracy of tuning. The structure so developed is the most suitable for realization of variable filters based on cascaded-identical-sub-filters structure and of adaptive filters for tracking or suppression of narrow-band signals.