Passivity properties of low-sensitivity digital filter structures

A general representation of a class of low passband sensitivity digital filter structures is proposed. The proposed representation for a transfer function of order consists of an -pair memoryless system terminated at -pairs by delays. The -pair system contains only adders and multipliers, and is described by an orthogonal transfer matrix. The set of terminating delays can be looked upon as an -pair system with transfer matrix . Certain wave digital filter structures, Gray-Markel lattice structures and the coupled-form biquadratic section belong to the general form advanced here. Several properties satisfied in these special cases are derived in a unified manner using the generalized representation. Also, a quantization scheme that makes the structure free from zero-input limit cycles even under time-varying conditions is advanced, unifying similar such results independently reported for the above well-known structures.