Postfiltering to equalize the effects of finite coefficient wordlength in digital filters

A linear-phase FIR postfilter is proposed as an equalizer to reduce the passband error of digital filters with fixed point coefficients. By representing a filter´s frequency magnitude response by a Fourier cosine series over a passband, a time-frequency dual is used to derive a simple relationship between the Fourier coefficient values and the tap weights of an FIR postfilter. It is shown that all but the largest Fourier components can be neglected and that the nonnegligible components can be truncated to a power of two. This results in a hardware efficient multiplierless postfilter where most of the taps are zero. Design examples are presented using multiplierless postfilters to equalize fixed wordlength filters such that the overall passband error is equivalent to a filter with infinite coefficient precision