JOURNAL OF COMPUTERS (JCP)
ISSN : 1796-203X
Volume : 2    Issue : 7    Date : September 2007

Optimization of FRM FIR Digital Filters Over CSD and CDBNS Multiplier Coefficient Spaces
Employing a Novel Genetic Algorithm
Patrick Mercier, Sai Mohan Kilambi, and Behrouz Nowrouzian
Page(s): 20-31
Full Text:
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Abstract
It is well known that frequency response masking (FRM) FIR digital filters can be designed to exhibit
very sharp-transition bands at the cost of slightly larger filter lengths as compared to the
conventional FIR digital filters. The FRM FIR digital filters permit efficient hardware implementations
due to an inherently large number of zerovalued multiplier coefficients in their transfer functions. The
hardware complexity of these FIR digital filters can be further reduced by employing computationally
efficient number systems for the representation of the constituent non-zerovalued multiplier
coefficients. This paper presents a novel genetic algorithm for the design and discrete optimization
of FRM FIR digital filters over the conventional canonical signed-digit (CSD) as well as the emerging
double base number system (DBNS) multiplier coefficient spaces. This genetic algorithm is based
on a pair of indexed look-up tables (LUTs) of permissible CSD/DBNS numbers whose indices form
a closed set under the genetic algorithm operations of crossover and mutation. The CSD/DBNS
values themselves permit pre-specified wordlengths and pre-specified number of non-zero bits.
The salient feature of the proposed genetic algorithm is that it automatically leads to legitimate
CSD/DBNS multiplier coefficients without any recourse to gene repair during optimization. The main
features of the proposed genetic algorithm are demonstrated through its application to the design of
a pair of lowpass and bandpass FRM FIR digital filters.

Index Terms
Frequency Response Masking Approach, Digital Filters, Genetic Algorithms, Optimization,
Canonical Signed Digit, Double Base Number System.