A fast algorithm for the recursive design of linear phase filters

One appropriate technique for the recursive design of linear phase filters is via a minimum mean square error estimation procedure. This paper presents a different parameterization of the problem, which enforces the linear phase structure at all stages of the procedure. The computational complexity of the resulting filter design algorithm is approximately one-half that of existing algorithms, when measured as the overall number of multiplications required. This algorithm in turn leads to a new linear phase realization, simpler than a linear phase lattice/ladder structure and exhibiting better numerical properties than a direct form implementation. The improvement in finite wordlength effects is illustrated by the example design of a lowpass filter.