Sigma-delta encoding for efficient equalization of prefilter based FIR filters

It is well known that the computational workload of finite impulse response (FIR) filters can be significantly reduced using the prefilter-equalizer approach. A technique for rounding the tap coefficients of the equalizer to a single power-of-two (or a small combination of powers-of-two) with little or no degradation in overall filter performance is described. Using error spectrum shaping, the equalizer coefficient truncation error is moved to higher frequencies where it is attenuated by the prefilter. The resulting equalizer requires no multiplications and is typically only of slightly higher order than an optimal direct form equalizer with infinite precision coefficients. Examples are given showing a 4×decrease in arithmetic complexity over previous prefilter-equalizer approaches and a 1.5×decrease over optimal interpolated FIR approaches