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 second-order Bode-type wave-digital (WD) variable-amplitude equalizers. The proposed first-order equalizer consists of one unit-delay and two digital multipliers and produces a fan-shaped magnitude-frequency response, while the proposed second-order equalizer consists of two unit-delays and three digital multipliers and produces a bump-shaped magnitude-frequency response. The salient feature of the resulting WD equalizers is that only a single digital variable multiplier is required to control the fan amplitude in the first-order equalizer and the bump amplitude in the second-orderequalizer without changing their other important magnitude-frequency response characteristics (e.g., the cut-off frequency in the fan equalizer and the centre frequency and quality factor in the bump equalizer). Moreover, these equalizers remain bounded-input bounded-output (BIBO) stable (under infinite-precision arithmetic) for all possible values of the variable multiplier. In addition, they exhibit the important practical feature that a geometrically symmetric change in the value of the variable multiplier causes a corresponding arithmetically symmetric change in the logarithmic magnitude-frequency response of the equalizer. Application examples are given to illustrate the main results.