Iterative Design of FIR Filters - Advances in Heuristic Signal Processing and Applications - page 144

used for the design of digital filters [ 6 ]. The simplest of these is the windowing
method [ 1 ]. In this method, the ideal impulse response is multiplied with a win-
dow function. Various kinds of window functions (Butterworth, Chebyshev, Kaiser,
etc.) can be used depending on the requirements of the ripples on the passband and
stopband, the stopband attenuation and the transition width. These various windows
limit the infinite length impulse response of the ideal filter into a finite window to
design an actual response. However, windowing methods do not allow sufficient
control of the frequency response in the various frequency bands and other filter pa-
rameters, such as transition width. The designer always has to compromise on one
or the other of the design specifications. In [ 20 ], a mixed integer linear program-
ming (MILP)-based approach for designing linear phase FIR filters is described.
However, the solution time in MILP-based algorithms increases exponentially as
the order of the filter increases. A branch-and-bound approach for designing hard-
ware platform-efficient FIR filters is described in [ 2 ]. Traditional design techniques
have design time and/or design parameter limitations. Many recent studies have
investigated different techniques for designing digital filters [ 3 , 11 , 12 , 16 , 17 ]. Be-
cause population-based stochastic search methods have proved effective in multidi-
mensional nonlinear environments, computational intelligence techniques, such as
neural networks [ 8 ], genetic algorithms (GAs) [ 1 , 7 ], immune algorithms [ 7 ], dif-
ferential evolution (DE) [ 9 , 18 ], and Particle Swarm Optimization (PSO) [ 7 , 10 ],
have been applied in the design of digital filters. Hybrid algorithms, which com-
bine features of different algorithms, or modified and mutation-based PSO algo-
rithms, which perform better than classical PSO, such as Quantum-behaved PSO
(QPSO) [ 5 , 6 ], Differential Evolution PSO (DEPSO) [ 13 ], and craziness-based
PSO [ 15 ], have also been applied for better parameter control and better approx-
imation to the ideal filter [ 6 ]. These algorithms, because they are multidimensional
optimization methods, can effectively consider the different constraints during filter
design. Finite Impulse Response (FIR) filters do not have feedback as do Infinite
Impulse Response (IIR) filters and hence are inherently stable. They can be easily
designed as linear phase filters. However, they require more memory and computa-
tional complexity than IIR filters to achieve the same performance.
Many modern applications already demand high computational speed and robust
solutions. Hence, traditional techniques and many computational intelligence algo-
rithms will also fail to meet future design requirements, which will prove even more
stringent. It is important to reduce the number of coefficients and still try to meet
other design requirements when it comes to implementing the digital filter in hard-
ware. Therefore, algorithms that have better convergence, that can perform more
consistently, and that can design filters with better frequency responses for fewer
coefficients are more likely to be applied in resource-constrained and performance-
critical applications. This chapter presents the application of PSO-QI [ 14 ], which
shows such a potential, for digital FIR filter design. Population based optimization
algorithms such as PSO-QI are probabilistic and not deterministic, so they require
multiple iterations for convergence. Digital filter design, as explained in this chap-
ter, is also a form of a parameter (coefficients) optimization process and hence is
iterative. The major contributions of this work are as follows: