Abstract: It is known that some families of digital filters may be represented by single multidimensional transfer functions called filter-generating functions. Previous examples of such filter-generating systems were related to the class of maximally flat FIR digital filters. The purpose of this paper is to show that the Chebyshev kernel used in the McClellan transformation of 1-D filters, and the Sylvester-type Hadamard transform, also known as the Walsh-Hadamard transform also possess simple multidimensional generating functions. Explicit formulas for the generating functions are derived and filter-generating systems for their implementation are discussed.
Key words: IIR digital filters, McClellan transformation, Hadamard transformation, filter generating function.