Digital Signal Processing Reference
In-Depth Information
H
c
2
hk
0
()
0
c
hk
0
()
H
2
0
c
H
d
2
1
0
hk
1
()
hk
1
()
H
d
2
1
FIGURE 13.36
Analysis using the dyadic subband coding structure.
c
2
H
0
c
+
H
2
0
d
H
2
+
c
0
1
d
H
2
1
FIGURE 13.37
Synthesis using the dyadic subband coding structure.
Now, let us study the DWT and IDWT in the following examples.
EXAMPLE 13.7
Given the sample values [4 2 1 0], use the Haar wavelets to determine the wavelet coefficients.
Solution:
Form the filter inputs:
21
1
2
c
2
ðkÞ¼2
2=2
½4210 ¼
0
The acquired Haar wavelet filter coefficients are listed as
1
1
1
1
p
p
p
p
h
0
ðkÞ¼
and
h
1
ðkÞ¼
The function is expanded by the scaling functions as
f ðtÞ
z
f
2
ðtÞ¼
N
k ¼
N
j=2
j
t kÞ
c
j
ðkÞ2
fð2
¼ 4 fð4tÞþ2 fð4t 1Þ1 fð4t 2Þþ0 fð4t 3Þ:
Search WWH ::
Custom Search