Finite Impulse Response Filters - Digital Signal Processing in Power System Protection and Control - page 92

(a)

0.5

h ()

0.4

0.3

0.2

0.1

0

-0.1

0 5 10 15 20

n

(b)

1 .2

H ( j ω )

1

1

2

0 .8

0 .6

0 .4

0 .2

0

0 200 400 600 800 1000

ωπ 2

Fig. 6.15 Impulse a and frequency b responses of the designed filter (Example 6.9); 1—original
filter spectrum, 2—spectrum modified by application of a smoothing window

H ð k Þ¼ exp ½ jkp ð N 1 Þ= N ¼ exp ð jkp19 = 20

for k ¼ 1 ; 2 ; 3

exp ½ j ð N k Þ p ð N 1 Þ= N ¼ exp ½ j ð 20 k Þ pN 1 = N for k ¼ 17 ; 18 ; 19 :

The above filter spectrum (Fig. 6.16 a) has been subjected to inverse Fourier
transformation, giving the following impulse response (filter coefficients):

h ð 0 Þ¼ h ð 19 Þ¼ 0 : 0928; h ð 1 Þ¼ h ð 18 Þ¼ 0 : 046; h ð 2 Þ¼ h ð 17 Þ¼ 0;
h ð 3 Þ¼ h ð 16 Þ¼ 0 : 0054;
h ð 4 Þ¼ h ð 15 Þ¼ 0 : 0654; h ð 5 Þ¼ h ð 14 Þ¼ 0 : 1249; h ð 6 Þ¼ h ð 13 Þ¼ 0 : 1121;
h ð 7 Þ¼ h ð 12 Þ¼ 0;
h ð 8 Þ¼ h ð 11 Þ¼ 0 : 1635; h ð 9 Þ¼ h ð 10 Þ¼ 0 : 2830;