A Technique for Synthesizing Digital Filters

In designing digital systems, one often faces the task of replacing a given analog filter by an equivalent digital filter. This paper proposes a method for synthesizing such digital filters in the time domain. It is assumed that the pulsed transfer function of the digital filter is a ratio of two rational polynomials. The coefficients are then determined by least-square fitting the digital filter to the analog filter's sampled input and output data. The resulting equations for computing the coefficients are linear. It is shown that the digital filter is essentially related to the analog filter, the sampling time, and the power spectrum of the signal being processed. If the signal is band-limited and the sampling frequency is sufficiently high, the digital filter can then be simply approximated by the Z transform of the analog filter multiplied by the sampling period.