language: en

Theory and Design of Multidimensional QMF Sub-Band Filters From 1-D Filters and Polynomials Using Transforms

I.A. Shah A.A.C. Kalker
Philips Research Laboratories,
P.O. Box 80.000, 5600 JA Eindhoven, The Netherlands
Net: kalker@prl.philips.nl, shah@prl.philips.nl

Abstract The paper presents the general theory of designing multidimensional Quadrature Mirror Filters (QMF), for use in sub-band coding (SBC) systems, using the McClellan transform [1]. It was recently shown that McClellan transform could be used to generate 2-D diamond shape QMF filters [2]. In this paper we will formalize the proofs of the diamond shape case, and generalize it to other shapes, sampling rasters and dimensions. Moreover we show that we do not really need the 1-D QMF filters: it is also possible and even more convenient to design QMF filter banks by performing transformations on a class of real valued polynomials. Examples are given of two dimensional diamond and fan-shape filters and three dimensional tetrad filters designed using this transformation technique.

1 Introduction