Efficient digit-serial rational function approximations and digital filtering applications

Continued fractions (CFs) efficiently compute digit-serial rational function approximations. Traditionally, CFs are used to compute homographic functions such as y=ax+b/cx+d, given continued fractions x, y, and integers a, b, c, d. Improvements in the implementation of CF algorithms open up their use to many digital filtering applications in both software and hardware. These improvements of CF algorithms include error control, more efficient number representation and the associated efficient conversions. Continued fractions have been applied to digital filters in the frequency domain. These techniques include methods to compute optimal coefficients for rational transfer functions of digital filters and the realization of ladder forms for digital filtering. We propose a time domain digital filtering technique that incorporates continued fraction arithmetic units. For the FIR filter example chosen, the proposed technique achieves a 45-50% reduction of the mean square error of the transfer function.