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
N
consists of an
(N + 1)
-pair memoryless system terminated at
N
-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 an
N
-pair system with transfer matrix
z^{-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.