Finite Impulse Response Filters - Digital Signal Processing in Power System Protection and Control - page 91

(a)

1

H ( k )

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

0 5 10 15 20

k

(b)

15

arg{ ( )} Hk

10

5

0

-5

-10

-15

0 5 10 15 20

k

Fig. 6.14 Magnitude a and phase b of the filter to be designed (Example 6.9)

8
<

1 for k ¼ 1 ; 2 ; 3 ; i : e : for f ¼ 50 ; 100 ; 150 Hz

j H ð k Þ j ¼ 1 for k ¼ 17 ; 18 ; 19 ; i : e : for ¼ 1000 150 ; 1000 100 ; 1000 50 Hz

:

0 for other frequencies :

From the requirement of linear phase it follows:

kp N N ¼ kp19 = 20 for k ¼ 1 ; 2 ; 3

arg ½ H ð k Þ ¼

ð N k Þ p N N ¼ð 20 k Þ p19 = 20 for k ¼ 17 ; 18 ; 19 :

Thus the complex filter spectrum (including both magnitude and phase) is
described as: