Discrete Lagrangian Methods for Designing Multiplierless Two-Channel PR-LP Filter Banks

  • Authors:

  • Benjamin W. Wah;Zhe Wu

  • Affiliations:

  • Department of Electrical and Computer Engineering and the Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA&semi/ Department of Computer Science a ...;Department of Computer Science and the Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA

  • Venue:
  • Journal of VLSI Signal Processing Systems
  • Year:
  • 1999

Quantified Score

Hi-index 0.00

Visualization

Abstract

In this paper, we present a new search method based on the theory ofdiscrete Lagrange multipliers for designing multiplierless PR (perfect reconstruction) LP (linear phase) filter banks.To satisfy the PR constraints, we choose a lattice structure that, undercertain conditions, can guarantee the resulting two filters to be a PR pair.Unlike the design of multiplierless QMF filter banks that representsfilter coefficients directly using PO2 (powers-of-two) form (also calledCanonical Signed Digit or CSD representation), we use PO2 forms to representthe parameters associated with the lattice structure.By representing these parameters as sums or differences of powers of two,multiplications can be carried out as additions, subtractions, and shifts.Using the lattice representation, we decompose thedesign problem into a sequence of four subproblems.The first two subproblems find a good starting point with continuousparameters using a single-objective, multi-constraint formulation.The last two subproblems first transform the continuous solution found by thesecond subproblem into a PO2 form, then search for a design in a mixed-integer space.We propose a new search method based on the theory of discreteLagrange multipliers for finding good designs, and study methods to improveits convergence speed by adjusting dynamically the relative weights betweenthe objective and the Lagrangian part.We show that our method can find good designs using at most four terms in PO2 form in each lattice parameter.Our approach is unique because our results are the first successful designs ofmultiplierless PR-LP filter banks. It is general because it is applicable to the design of other types of multiplierless filter banks.