Computationally fast lattice bilinear digital ladder filters with comparison to circulator WDFs

Abstract

This paper considers a modified variant of the lossless digital integrator lattice filter structure presented in [l, 2, 31, which in [l] is also labeled lattice bilinear digital ladder filter (BDLF). It is shown that the structure easily can be modified so that the critical loop reduces from two multipliers to one. This has the potential of significantly improving the computational speed when the filter is implemented directly in hardware. Two test filters of the modified BDLF structure are compared to three-port circulator lattice wave digital filters (WDF), which also have critical loops of only one multiplier. It is shown that for the test filters, the BDLF realizations are similar to the WDF realizations regarding multiplier wordlength requirements, while they are superior regarding quantization noise and structural complexity.

Suppression of overflow limit cycles in LDI all-pass/lattice filters

“…1. It is identical to that in [1], except that delayed and nondelayed integrators are interchanged. This removes the extra delay from u to y present in the previous structure.…”

“…Making 1 = 0 corresponds (see [1], [10]) to removing the resistance of the passive prototype, thus making the filter lossless.…”

“…This scaling is related to that used for wave digital filters (with multipliers k and 1=k inserted in the branches interconnecting two adaptors) [3] and, clearly, does not alter the transfer function of the ALF. Normally, (see [1] and Section IV) k i = 2 0b < 1, i.e., scaling by k i implies b i binary right shifts. Repeating steps similar to those above, the following theorem can be proven.…”

“…Consider the state-space quarter-plane model of a two-dimensional (1) represents overflow nonlinearities and T denotes the transpose. It is understood that system (1) has a finite set of initial conditions, i.e., there exist two positive integers p and q such that x v (k; 0) = 0; k p; x h (0; l) = 0; l q.…”

“…In [1] it is shown that system (1) will be globally asymptotically stable if there exists a positive definite diagonal matrix D such that D 0 A T DA > 0 (2) where '>' signifies that the matrix is positive definite. Condition (2) is based on the sector information of the overflow nonlinearities, namely, the sector [01; 1].…”