The general theory of designing multidimensional quadrature mirror filters (QMF) for use in sub-band coding systems using the McClellan transform [1] is presented. It was recently shown that the McClellan transform could be used to generate 2-D diamond-shape QMF filters [2]. The proofs of the diamond-shape case are formalised and generalise to other shapes, sampling rasters and dimensions. It is 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.