Efficient Digit Serial Rational Function Approximations 
            and Digital Filtering Applications 
[Asilomar Conference, Nov. 1999] 

Oskar Mencer, Martin Morf, Albert Liddicoat, Michael J. Flynn


Abstract

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. Recent 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.