Heuristic Optimal Design of Multiplier-less Digital Filter - Advances in Heuristic Signal Processing and Applications - page 255

Fig. 11.9 The desired
frequency response

The transfer function of designed CSD coded IIR filter is then described as:

0 . 125 z − 1

− −

0 . 49902

=

H(z)

0 . 375 z − 2 .

(11.21)

1 z − 1 − 1 . 2505 + −

The frequency response of the target IIR filter and the designed IIR filter are
depicted in Fig. 11.10 . It can be seen that the designed frequency response is very
close to that of the desired filter. Moreover, the poles of the transfer function of the
IIR filter are depicted in Fig. 11.11 . It is also obvious that all the poles lie inside the
disk D( 0 . 3 , 0 . 7 ) . That is, the CSD coded IIR filter is robustly D( 0 . 3 , 0 . 7 ) -stable.

Table 11.5 Parameters of GA

Parameter Value

selection method roulette wheel selection

number of chromosomes in each generation 40

bit length for each chromosome 90

crossover probability 0.9

mutation probability 0.08

No. of generations 35000

Table 11.6 CSD code of the coefficients of the designed IIR filter

Coefficients Real number code CSD code (a sign bit in the left-end position for each k i )

a o − 1 . 2505 100000 100010 101001

a 1 1 000000 010010 100000

a 2 − 0 . 375 100010 100010 100000

a 3 − 0 . 49902 100001 001000 100001

a 4 − 0 . 125 100010 0000001 00001