On the design of optimum FIR low-pass filters with even impulse response duration

A great deal of attention has been given recently to the theory of designing optimum, linear phase, finite impulse response (FIR) low-pass digital filters where N, the filter impulse response duration, was odd. In this paper it is shown that the inclusion of optimal filters with even values of N gives additional flexibility to the general filter design problem. In particular, it will be shown that for certain ranges of filter cut-off frequencies, length N filters (N may be either even or odd) have smaller ripple than length (N + 1) filters. Finally, the general properties of optimal filters with even values of N are discussed. These include: filter types, scaling procedures, Chebyshev solutions, and symmetry of the basic design curves. The necessary modifications to existing design programs for filters with odd values of N to give filters with even values of N are also discussed.