Passivity properties of low-sensitivity digital filter structures
Palghat P. Vaidyanathan, Sanjit K. Mitra · IEEE Transactions on Circuits and Systems · 1985
A general representation of a class of low passband sensitivity digital filter structures is proposed. The proposed representation for a transfer function of orderNconsists of an(N + 1)-pair memoryless system terminated atN-pairs by delays. The(N + 1)-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 anN-pair system with transfer matrixz^{-1}{\bf 1}. 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.