An alternative approach to the design and synthesis of higher-order Bode-type variable-amplitude wave-digital equalizers

This paper presents an alternative approach to the design and synthesis of higher-order Bode-type variable-amplitude (VA) wave-digital (WD) equalizers. The proposed approach is based on, (a) the development of a theoretical method for the derivation of a corresponding VA analog equalizer shaping transfer function starting from a set of high-level system design specifications, (b) the development of a synthesis approach for a suitable analog prototype reference network for a WD equalizer realization requiring one single variable digital multiplier only, and (c) the development of a method for the transformation of the analog prototype reference network to the desired VA WD equalizer without making any recourse to the use of three-port series or parallel adapters inherent in the conventional WD realization techniques. The resulting VA WD equalizers permit the continuous variation of the WD equalizer transfer function from the shaping transfer function to its inverse through the use of a single variable digital multiplier. In addition, they exhibit the important practical feature that a geometrically symmetric change in the value of the variable digital multiplier causes a corresponding arithmetically symmetric change in the logarithmic magnitude-frequency response of the WD equalizer. An application example is given to illustrate the main results.