The design and application of optimal FIR fractional-slope phase filters

A new technique for the design of FIR fractional-slope phase filters based on Chebyshev approximation is described and analyzed. The technique results from a formulation of the problem which satisfies the Haar condition, thus allowing the use of the efficient Remez exchange algorithm. The new design is implemented with a modification of the McClellan-Parks-Rabiner FIR filter design program. The resulting fractional-slope phase filters are shown to have a complex error function that is essentially equiripple in magnitude. The new technique may be used for designing parallel elements of a multirate filter, such as the polyphase interpolation filter, or for stand-alone filters used as fractional-slope phase shifters. The advantages of the new technique are the simplicity and numerical stability of the design program and the lack of restrictions on phase slope specification.