Finite precision design of linear-phase fir filters

The FIR (finite impulse response) filter is an essential tool for a large number of applications in communication. In this paper we consider the design of linear-phase FIR digital filters with finitely precise coefficients. Coefficient inaccuracy is known to degrade the frequency response of band-select FIR filters, especially in the stopband region. We derive a bound on the attainable stopband attenuation, and we also develop techniques for designing FIR filters with finitely precise coefficients. Mixed-integer programming algorithms are presented to select finitely precise coefficients for a filter that best approximates an arbitrary magnitude characteristic in the minimax sense. Our method generates a number of possible solutions including that of simple rounding or truncation and then selects the best finitely precise coefficients from this set. In this way, significant improvement in the filter performance is gained over methods that simply round or truncate the infinitely precise coefficients. We also show how integer programming can be used to design filters with powers of two coefficients. Such filters are easier to mechanize since they do not require multipliers.