Digital Signal Processing Reference
In-Depth Information
13.22. Given the 4-tap Daubechies wavelet coefficients
h
0
(
k
)
¼
[0.483 0.837 0.224
0.129]
determine
h
1
ðkÞ
and plot magnitude frequency responses for both
h
0
ðkÞ
and
h
1
ðkÞ
.
13.23. Given the sample values [8
2 4 1], use the Haar wavelet to determine the level-2 wavelet
coefficients.
13.24. Given the sample values [8
2430
1
2 0], use the Haar wavelet to determine the level-
3 wavelet coefficients.
13.25. Given the level-2 wavelet coefficients [4 2
1 2], use the Haar wavelet to determine the
sampled signal vector
f ðkÞ
.
13.26. Given the level-3 wavelet coefficients [4 2
1 2 0 0 0 0], use the Haar wavelet to determine
the sampled signal vector
f ðkÞ
.
13.27. Given the level-1 wavelet coefficients [4 2
1 2], use the Haar wavelet to determine the
sampled signal vector
f ðkÞ
.
13.28. The four-level DWT coefficients are given as follows:
W
¼
[100 20 16
5
342
64612
302
1]
List the wavelet coefficients to achieve each of the following compression ratios:
a. 2:1
b. 4:1
c. 8:1
d. 16:1
13.10.1
MATLAB Problems
Use MATLAB to solve Problems 13.29 to 13.31.
13.29.
Use the 16-tap PR-CQF coefficients and MATLAB to verify the following conditions:
N
1
k ¼
0
h
0
ðkÞh
0
ðk þ
2
nÞ¼dðnÞ
rð
2
nÞ¼
RðzÞþRðzÞ¼
2
Plot the frequency responses for
h
0
ðkÞ
and
h
1
ðkÞ
.
13.30.
Use the MATLAB functions provided in
Section 13.8
[dwt(), idwt()] to verify Problems
13.23-13.27.
13.31.
Consider a 20-Hz sinusoidal signal plus random noise sampled at 8,000 Hz with 1,024 samples:
xðnÞ¼
100 cos
ð
2
p
20
nTÞþ
50
randn
where
T ¼
1
=
8
;
000 seconds and
randn
is a random noise generator with a unit power and
Gaussian distribution.
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