Design of first- and second-order Bode-type wave digital variable amplitude equalizers

This paper presents a synthesis technique for the design of first- and seco nd-order Bode-type wave-digital (WD) variable-amplitude equalizers. The pro posed first-order equalizer consists of one unit-delay and two digital mult ipliers and produces a fan-shaped magnitude-frequency response, while the p roposed second-order equalizer consists of two unit-delays and three digita l multipliers and produces a bump-shaped magnitude-frequency response. The salient feature of the resulting WD equalizers is that only a single digita l variable multiplier is required to control the fan amplitude in the first -order equalizer and the bump amplitude in the second-order equalizer witho ut changing their other important magnitude-frequency response characterist ics (e.g., me cut-off frequency in the fan equalizer and the centre frequen cy and quality factor in the bump equalizer). Moreover, these equalizers re main bounded-input bounded-output (BIBO) stable (under infinite-precision a rithmetic) for all possible values of the variable multiplier. In addition, they exhibit the important practical feature that a geometrically symmetri c change in the value of the variable multiplier causes a corresponding ari thmetically symmetric change in the logarithmic magnitude-frequency respons e of the equalizer. Application examples are given to illustrate the main r esults.