Finite Impulse Response Filter Design - Digital Signal Processing: Fundamentals and Applications - page 232

0.2

0.1

0

-4 -3 -2 -1 0 1 2 3 4

Sample number n

0.2

0.1

0

-4 -3 -2 -1 0 1 2 3 4

Sample number n

FIGURE 7.10

Plots of FIR noncausal coefficients and windowed FIR coefficients in Example 7.4.

1 p
3

w ham ð1Þ¼0:54 þ 0:46 cos ¼ 0:77

2 p
3

w ham ð2Þ¼0:54 þ 0:46 cos ¼ 0:31

3 p
3

w ham ð3Þ¼0:54 þ 0:46 cos ¼ 0:08

Applying the Hamming window function and its symmetric property to the filter coefficients, we get

h w ð0Þ¼hð0Þ$w ham ð0Þ¼0:25 1 ¼ 0:25

h w ð1Þ¼hð1Þ$w ham ð1Þ¼0:22508 0:77 ¼ 0:17331 ¼ h w ð1Þ

h w ð2Þ¼hð2Þ$w ham ð2Þ¼0:15915 0:31 ¼ 0:04934 ¼ h w ð2Þ

h w ð3Þ¼hð3Þ$w ham ð3Þ¼0:07503 0:08 ¼ 0:00600 ¼ h w ð3Þ

b. Noncausal impulse responses hðnÞ and h w ðnÞ are plotted in Figure 7.10 .
We observe that the Hamming window does its job and weights the FIR filter coefficients to zero gradually at
both ends. Hence, we can expect a reduced Gibbs effect in the magnitude frequency response.