Design of computationally efficient narrow-band linear-phase FIR filters

This paper considers the design of computationally efficient narrow-band linear-phase finite-impulse response (FIR) filters with the transfer function of the form H(z) = F(z^M)G(z), where F(z) is a linear-phase FIR transfer function. G(z) is constructed as a cascade of two linear-phase multiplier-free FIR filter building blocks. The first blocks are of the form 2^-P_r[1-z^-K_r/(1-z^-1) with different values of the integers K_r. In these blocks the P_r´s are integers. The second blocks are of the form ( 1/2 )(1 + z^-L_r) with different values of the integer L_r. Given the filter specifications, the problem is to find these building blocks, the order of F(z), and the integer M in F(z^M) and to optimize the impulse-response values of F(z) so that the arithmetic complexity is minimized. It is shown how F(z) can be conveniently optimized with the aid of the fast Remez multiple exchange algorithm. For multiplier-free designs, the overall filter should exceed the given criteria in order to enable one to quantize the coefficient values of F(z^L) to have two powers-of-two representations. Two examples taken from the literature show that the optimized proposed filters outperform other existing filter designs meeting the same criteria.