Stability and transient behavior of Bode-type variable-amplitude digital equalizers with dynamic variable multiplier variations

In a previous publication, the theoretical basis provided by Kharitonov´s stability theorem was exploited and applied to the development of a novel BIBO stability condition for general-order Bode-type variable-amplitude (VA) digital equalizers. This was achieved under the assumptions, (a) that the VA digital equalizer operates under infinite precision arithmetic, and (b) that it operates under “static” variable digital multiplier variations (i.e. variations which occur slowly or only after the transients resulting from the “dynamic” variations of the digital multiplier have died down to negligible levels). The present paper is concerned with an extension of the results to the investigation of the effect of “dynamic” variations of the variable digital multiplier on the stability and transient signal behaviour of the Bode-type VA digital equalizers both under infinite-precision as well as finite-precision digital equalizer operations. An analytical relationship is also derived for the estimation of the time required for the equalizer output signal transients to reduce to a specified negligible level. An application example is given to illustrate the practical application of the main results