Subband- and Wavelet-Based Coding - Digital Signal Processing: Fundamentals and Applications - page 654

Table 13.2 Typical Wavelet Filter Coefficients h 0 ðkÞ

Haar Daubechies 4 Daubechies 6 Daubechies 8

0.707106781186548
0.707106781186548

0.482962913144534
0.836516303737808
0.224143868042013

0.332670552950083
0.806891509311093
0.459877502118492

0.230377813308896
0.714846570552915
0.630880767929859

0.129409522551260 0.135011020010255 0.027983769416859

0.085441273882027
0.035226291885710

0.187034811719093
0.030841381835561
0.032883011666885

0.010597401785069

Figure 13.33 shows each component at resolution j ¼ 1 and the constructed scaling function fðtÞ .
The original scaling function fðtÞ is also included as shown in the last plot for comparison.
With the given coefficients h 0 ðkÞ

and applying Equation (13.45) , we can obtain the wavelet

coefficients h 1 ðkÞ as
h 1 ð 0 Þ¼ 0 : 1294 ; h 1 ð 1 Þ¼ 0 : 2241 ; h 1 ð 2 Þ¼ 0 : 8365 ;

and h 1 ð 2 Þ¼ 0 : 4830

1 2

0.5 1

0 0

-0.5 -1

0 1 2 3 0 1 2 3

0.5 0.5

0 0

-0.5 -0.5

0 1 2 3 0 1 2 3

2 2

1 1

0 0

-1 -1

0 1 2 3 0 1 2 3

Time (s ec . ) Time (s ec . )

FIGURE 13.33

Constructed 4-tap Daubechies father wavelet.