Atomic Functions ha(x) in Digital to Analog Conversion

A new method of atomic functions approximation by rational fractions is proposed. The method is based on approximation of Cauchy integral by Riemann sum and involves the problem of integration contour optimization. Obtained rational fractions may be used for construction of transfer function of a stable analog filter with rapidly decaying impulse response. Results of numerical experiment demonstrating advantages of new filters applied to digital to analog conversion are presented.