Iterative Design of FIR Filters - Advances in Heuristic Signal Processing and Applications - page 150

Ta b l e 7 . 1 Algorithm specifications

Parameter Symbol Value

Population size S 25

Number of iterations 5000

Number of trials 50

Inertia w linearly decreasing from 0.9 to 0.4

Cognitive constant c 1 2

Social constant c 2 2

Creativity coefficient β linearly increasing from 0.5 to 1

Crossover rate 0.5

Ta b l e 7 . 2 Filter specifications

Filter Parameter Symbol Value

LP, HP Passband normalized cutoff frequency ω p 0.3

LP, HP Stopband normalized cutoff frequency ω s 0.35

BP, BS Normalized lower cutoff frequency ω l 0.3

BP, BS Normalized upper cutoff frequency ω u 0.7

LP,HP,BP,BS Passbandripple δ p 0.1

LP, HP, BP, BS Stopband ripple δ p 0.01

LP, HP, BP, BS Number of coefficients N 21

LP, HP, BP, BS Number of samples T 256

LP, HP, BP, BS Weighting vector G 1

ison of the MSEs obtained by the two approaches. This is shown in the row labeled
“Avg Case I” (italicized) under the columns for Case II. This comparison of the two
cases shows that lower values of MSE are obtained when using I 1 . This suggests
that trying to approximate a filter to the ideal filter results is better than trying to ap-
proximate it to a given design specification. The filters designed by the CLS method
are also evaluated using fitness functions of both cases (shown in columns ' I 1 ' and
' I 2 '). The comparison of these MSEs with those obtained with CLS also confirms
that using PSO-QI in Case I achieves better results. The lowest MSE values for Case
I, and the lowest standard deviations values for Cases I and II, are shown in bold for
different iterations. The consistent performance of the PSO-QI algorithm is demon-
strated in the results by the lower standard deviation values obtained in the final
iteration. The maximum ripples in the passband and stopband obtained for different
filters are also presented.
These show that none of the design approaches could meet the specification ex-
actly. This is mainly because the algorithms compromised on transition width in
order to best meet the other requirements for designing an FIR filter of a given or-
der. Evolutionary algorithms are still able to design filters with narrower transition