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.