Page 393 - Analog and Digital Filter Design

390 Analog and Digital Filter Design

The Kaiser-Bessel window, with a = 3.0, produces a first side-lobe attenuation
of 70dB. The coefficients are veiy similar to those of the four-term Blackman-
Harris window:
h(n) = 0.40243+0.49804c0s[ -1 2a n +o.09831cos[ 4
2a.
2n
N
+ o.oo122cos[T] 2n. 3n

where n = -(N - 1)/2,. . . ,-l,O,l, . . . ,(N - 1)/2.

Once again, when time-shifted, the second and fourth terms change sign:

2a.n
Iz(n> = o.40243-o.49804cos[l,]+o.09831cos[~] 2n.2n
2a.
- o.oo122cos[~]
3n
where n = 0,1, . . . , (N - 1)/2.

Summary of Fixed FIR Windows
Table 16.1 gives details of the fixed window filters discussed in this chapter.

WINDOW (-3dB) Bandwidth Attenuation

Rectangular 0.89 -13.2
Bartlett 1.28 -27
Hamming 1.3 -43
Von Hann 1.54 -35
Blackman 1.52 -5 1
Exact Blackman 1.42 -69
3-term Blackman-Harris 1.56 -6 1
4-term Blackman-Harris 1.74 -74
3-term Harris-Nutall 1.66 -67
4-term Harris-Nutall 1.9 -92

Table 16.1
Window Bandwidth and Stopband Attenuation

Number of Taps Needed by Fixed Window Functions

1 Find the steepness of the slope between passband and stopband.
The number of taps needed depends on the steepness of the slope
between the passband and the stopband. In lowpass and highpass
filter designs this is the difference between the passband and the stop-