Finite Impulse Response Filter Design - Digital Signal Processing: Fundamentals and Applications - page 231

1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

-40 -30 -20 -10 0 10 20 30 40

Number of samples

FIGURE 7.9

Shapes of window functions for the case of 2M þ 1 ¼ 81. “o” line, triangular window; “þ” line, Hanning
window; solid line, Hamming window; dashed line, Blackman window.

EXAMPLE 7.4
Given the calculated filter coefficients
hð0Þ¼0:25; hð1Þ¼hð1Þ¼0:22508; hð2Þ¼hð2Þ¼0:15915; hð3Þ¼hð3Þ¼0:07503
a. apply the hamming window function to obtain windowed coefficients h w ðnÞ;
b. plot the impulse response hðnÞ and windowed impulse response h w ðnÞ.
Solution:
a. Since M ¼ 3, applying Equation (7.18) leads to the window sequence

3 p
3

w ham ð3Þ¼0:54 þ 0:46 cos ¼ 0:08

2 p
3

w ham ð2Þ¼0:54 þ 0:46 cos ¼ 0:31

1 p
3

w ham ð1Þ¼0:54 þ 0:46 cos ¼ 0:77

0 p
3

w ham ð0Þ¼0:54 þ 0:46 cos ¼ 1