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The general theory of designing multidimensional quadrature mirror filters (QMF) for use in sub-band coding systems using the McClellan transform is presented. It was recently shown that the McClellan transform could be used to generate 2-D diamond-shape QMF filters (de Lameillieure et al. 1991). The proofs of the diamond-shape case are formalised and generalised to other shapes, sampling rasters...