An exact BIBO stability condition for Bode-type variable-amplitude digital equalizers

In previous publications, the authors presented novel techniques for the design and realization of Bode-type variable-amplitude digital equalizers. The frequency response of the resulting variable-amplitude digital equalizers can be varied from that of an arbitrary shaping transfer function to its inverse by varying the value of a single variable digital multiplier. This paper is concerned with the development of an exact bounded-input bounded-output (BIBO) stability condition for general-order Bode-type variable-amplitude digital equalizers. The salient feature of the resulting BIBO stability condition is that it guarantees the stability of the Bode-type variable-amplitude digital equalizers over an entire range of values for the constituent variable digital multiplier. Moreover, this BIBO stability condition can simply be evaluated by examining the shaping transfer function associated with the variable-amplitude digital equalizer proper