Novel realizability conditions for the exact design of second-order Bode-type variable-amplitude digital equalizers

This paper presents a set of novel realizability conditions for the direct discrete-time z-domain design of second-order Bode-type variable-amplitude digital equalizers. These realizability conditions take into account both the structure of the resulting Bode-type variable-amplitude digital equalizers as well as their BIBO stability. The proposed realizability conditions find applications not only in the computational design (by enumeration) of variable-amplitude digital equalizers but also in their analytical design. The salient feature of the resulting digital equalizers is that their frequency response may be varied continuously from that of a specified shaping transfer function to its inverse by varying the value of a single variable multiplier. An example is given to illustrate the application of the proposed realizability conditions to the design of the corresponding bump digital equalizers