Design of narrow-band FIR filter with low group delay and piecewise polynomial impulse response

This paper presents a design method for piecewise polynomial digital filter with very low group delay. The first step to design such filter is to determine filter coefficient of the approximately linear phase, low delay and quasi-equiripple FIR lowpass by using existing design procedure. After that, the polynomial coefficients are obtained using transform which is derived here. The main advantage of the FIR filter with piecewise polynomial impulse response is in the fact that it can be efficiently implemented by using recursive or Farrow structure, depending on the application. In this way, the number of multiplications can be significantly reduced compared to the conventional FIR filter.