Finite Impulse Response Filter Design - Digital Signal Processing: Fundamentals and Applications - page 241

FIGURE 7.14

Lowpass filter frequency domain specifications.

Next, we illustrate the design for customer specifications in practice. Given the required stopband
attenuation and passband ripple specifications shown in Figure 7.14 , where the lowpass filter speci-
fications are given for illustrative purposes, the appropriate window can be selected based on the
performance of the window functions listed in Table 7.7 . For example, the Hamming window offers
a passband ripple of 0.0194 dB and stopband attenuation of 53 dB. With the selected Hamming
window and the normalized transition band defined in Table 7.7 ,

.

Df ¼ f stop f pass

f s (7.22)

TABLE 7.7 FIR Filter Length Estimation Using Window Functions
(normalized transition width Df ¼jf stop f pass j=f s )

Window Function
wðnÞ

Passband
Ripple (dB)

Stopband
Attenuation (dB) Window Type ,LM £ n £ M Window Length N

Rectangular 1 N ¼ 0 : 9 =Df 0.7416 21

5 cos pn
M

Hanning 0 : 5 þ 0 : N ¼ 3 : 1 =Df 0.0546 44

46 cos pn
M

Hamming N ¼ 3 : 3 =Df 0.0194 53

0 : 54 þ 0 :

5 cos np
M

Blackman N ¼ 5 : 5 =Df 0.0017 74

0 : 42 þ 0 :

08 cos 2

np
M

þ 0 :