New approach to the design of fir digital filters

This paper presents a new approach to designing finite impulse response (FIR) digital filters. The design algorithm is based on the least mean square (LMS) criterion in the time domain to calculate the filter coefficients using the weighted gain peak errors to adjust the LMS cost function. The filter responses are optimum in the sense that the maximum gain error is minimised. The design procedure accommodates the entire range of linear phase FIR filter specifications. The flexibility and optimality of the LMS approach is demonstrated with a wide variety of examples, including the classic extraripple, scaled extraripple and equiripple cases of linear phase and examples of nonlinear phase. To date the only two algorithms that have been able to design the full range of linear phase filters are based on the Cheby¿chev polynomial approach, namely Remez exchange and linear programming.