Subband- and Wavelet-Based Coding - Digital Signal Processing: Fundamentals and Applications - page 662

High frequency
(Large j, small scale=2

j

)

Low frequency
(Small j, large scale=2

j

)

Time

FIGURE 13.40

Time-frequency plane.

the DWT cannot achieve good resolutions in both frequency and time at the same time. The time-
frequency plot of the DWT amplitudes in terms of their intensity is shown in Figure 13.39 (b), and the
time and frequency plane for the DWT is shown in Figure 13.40 .

EXAMPLE 13.8
Given the wavelet coefficients obtained using the Haar wavelet filters

5
4

7
4

1 1

½c 0 ð0Þd 0 ð0Þd 1 ð0Þd 1 ð1Þ ¼

p p

2

perform the IDWT.
Solution:
From Equation (13.55) we get

N N

c 1 ðkÞ¼ c 0 ðmÞh 0 ðk 2mÞþ d 0 ðmÞh 1 ðk 2mÞ

m¼ N m¼ N

Then we recover coefficients c 1 ðkÞ as
c 1 ð0Þ¼ N
m¼ N

c 0 ðmÞh 0 ð2mÞþ N
m¼ N

d 0 ðmÞh 1 ð2mÞ

p
2

¼ c 0 ð0Þh 0 ð0Þþd 0 ð0Þh 1 ð0Þ¼ 5

4 1

p þ 7

4 1 p ¼ 3

c 1 ð1Þ¼ N
m¼ N

c 0 ðmÞh 0 ð1 2mÞþ N
m¼ N

d 0 ðmÞh 1 ð1 2mÞ

¼ c 0 ð0Þh 0 ð1Þþd 0 ð0Þh 1 ð1Þ¼ 5

4 1

p þ 7

1 2 ¼ 1

2

4

p

p

MATLAB verification using Figure 13.37 is given as
>> c1¼fconv([1 1]/sqrt(2),[5/4 0])þfconv([1 1]/sqrt(2),[7/4 0])
c1 ¼ 2.1213 0.3536