Low-complexity linear phase fir filters in cascade form

The design of low complexity finite impulse response (FIR) filters in a single-stage direct form or transposed direct form has reached a certain limitation since various multiplierless techniques have been proposed and explored. In addition, further investigations have shown that, instead of minimizing the number of adders used to implement the filter, it makes more sense to reduce the adder depth (AD) of the multiplier block (MB) from a power consumption point of view. Therefore, filters in cascade form deserve more attention because of the possibility of achieving even lower AD within each subfilter. In this paper, an algorithm is proposed for the design of linear phase FIR filters in cascade form with discrete coefficients. The proposed algorithm designs the coefficients of the subfilters simultaneously in integer space and finds all the possible discrete valued solutions. We show by an example that it is possible to design a filter using even smaller effective wordlength (EWL) and lower AD, whereas the total number of adders used to implement the overall filter is also kept minimum.