Universal maximally flat lowpass FIR systems

The family of FIR digital filters with maximally flat magnitude and group d elay response is considered. The filters were proposed by Baher, who furnis hed them with an analytic procedure for derivation of their transfer functi on. The contributions of this paper are the following. A simplified formula is presented for the transfer function of the filters, The equivalence of the novel formula with a formula that is derived from Baher's analytical pr ocedure is proved using a modern method for automatic proof of identities i nvolving binomial coefficients. The universality of Baher's filters is then established by proving that they include linear-phase filters, generalized half-band filters, and fractional delay systems, In this way, several clas ses of maximally flat filters are unified under a single formula, The gener ating function of the filters is also derived. This enables us to develop m ultiplierless cellular array structures for exact realization of a subset o f the filters. The subset that enjoys such multiplierless realizations incl udes linear-phase filters, some nonsymmetric filters, and generalized halfb and filters, A procedure for designing the cellular array structures is als o presented.