Digital Signal Processing Reference
In-Depth Information
Chapter 10
Particle Swarm Optimization of Highly Selective Digital
Filters over the Finite-Precision Multiplier Coefficient
Space
Seyyed Ali Hashemi and Behrouz Nowrouzian
Additional information is available at the end of the chapter
http://dx.doi.org/10.5772/52196
1. Introduction
Digital filters find wide variety of applications in modern digital signal processing systems [
1
,
2
]. As
a result of the recent progress in such systems, there is an ever growing demand for sharp transition
band digital filters. These narrow transition bandwidth digital filters are usually designed by using the
frequency response masking (FRM) approach [
3
]. The computational efficiency of the FRM technique
makes it suitable for different applications, e.g. in audio signal processing and data compression [
4
].
Practical design of digital filters is based on optimization for satisfying the given design specifications
together with the hardware architecture. However, the optimization may be carried out in terms of
fixed configurations but variable multiplier coefficient values. On the other hand, the problem may
concern the optimization of the hardware architecture without taking the multiplier coefficient values
into consideration.
In order to optimize the given design specifications, the multiplier coefficient values can be determined
in infinite precision by using hitherto optimization techniques. However, in an actual hardware
implementation of the digital filters, the infinite precision multipliers should be quantized to their
finite precision counterparts, but these finite precision multiplier coefficients may no longer satisfy
the given design specifications. Consequently, from a hardware implementation point of view, there is a
need for finite precision optimization techniques, capable of finding the optimized digital filter rapidly
while keeping the computational complexity at a desired level. In principle, there exist two different
techniques for the optimization of digital filters, namely, gradient-based and heuristic optimization
approaches.
Gradient-based optimization techniques have been studied widely. In [
5
], an integer programming
technique was developed for the optimization of digital filters over a discrete multiplier coefficient
