Design and implementation of narrow-band linear-phase FIR filters with piecewise polynomial impulse response

The transfer function of these filters is a parallel connection of several branches with transfer functions of the form G_l(z^L)F_l(z), where the length of each F _l(z) is L. It is shown that by properly selecting the F_l (z)´s the overall impulse response can be divided into several blocks of L samples in such a manner that in each block the impulse response is a polynomial of a given degree. The degree is one less than the number of branches, whereas the overall length of the impulse response is N=ML, where M is the length of the G_l(z)´s. Efficient implementation forms are proposed for the overall filter. Examples are included illustrating the efficiency of the proposed approach in implementing narrow-band linear-phase FIR filters