On the design of multidimensional FIR filters by transformation

This paper studies the applicability and limitations of the McClellan transformation method and, as a result, extends this method so that new types of one-dimensional filters can be transformed and new types of multi-dimensional filters can be designed. For this purpose, a new expression for the frequency response of an arbitrary one-dimensional filter is derived in terms of Chebyshev polynomials and other introduced polynomials satisfying recurrence formulae. The main objective is to identify which prototype filters can be transformed, determine what types of symmetry can be designed, and present procedures for transforming the new identified prototypes as well as rules for achieving the possible symmetries