Response error estimates for FIR digital filters with floating point coefficients

Response error estimates are derived for direct-form FIR (finite impulse response) digital filters having low-pass, high-pass, and bandpass characteristics. Simple-to-apply formulas are obtained on the basis of two observations: first, that the discontinuous relationships between a floating can be replaced by a continuous approximation; and secondly, that in the classes of filter considered, the impulse response possesses a closed form. Formulas that show the effect of wordlength, filter order, and filter bandwidth are derived. Simulation studies that confirm these estimates are reported