Subband- and Wavelet-Based Coding - Digital Signal Processing: Fundamentals and Applications - page 664

EXAMPLE 13.9
Given the sample values [4 2 1 0], use the provided MATLAB DWT (dwt.m) and IDWT (idwt.m) and specified
wavelet filter to perform the DWT and IWDT without using the scale factor 2 j=2 .
a. Haar wavelet filter
b. 4-tap Daubechies wavelet filter
Solution:
a. From Table 13.2 , the Haar wavelet filter coefficients are

1 2

1

h 0 ¼ p

p

Applying the MATLAB functions dwt() and idwt() , we have
>> w¼dwt([1/sqrt(2) 1/sqrt(2)],[4 2 1 0],2)'
w ¼ 2.5000 3.5000 1.4142 0.7071

>> f¼idwt([1/sqrt(2) 1/sqrt(2)],w,2)'
f ¼ 4.0000 2.0000 1.0000 0

b. From Table 13.2 , the 4-Tap Duabechies wavelet filter coefficients are
h0¼[0.482962913144534 0.836516303737808 0.224143868042013 0.129409522551260]

MATLAB program verification is demonstrated as follows:
>> w¼dwt([0.482962913144534 0.836516303737808 0.224143868042013 0.129409522551260],
[4 2 10],2)'
w ¼ 2.5000 2.2811 1.8024 2.5095

>> f¼idwt([0.482962913144534 0.836516303737808 0.224143868042013 0.129409522551260],
w,2)'
f ¼ 4.0000 2.0000 1.0000 0

13.7 WAVELET TRANSFORM CODING OF SIGNALS
We can apply the DWT and IWDT for data compression and decompression. The compression and
decompression involves two stages, that is, the analysis stage and the synthesis stage. At the analysis
stage, the wavelet coefficients are quantized based on their significance. Usually, we assign more bits
to the coefficient in a coarser scale, since the corresponding subband has larger signal energy and low
frequency components. We assign a small number of bits to a coefficient that resides in a finer scale,
since the corresponding subband has lower signal energy and high frequency components. The
quantized coefficients can be efficiently transmitted. The DWT coefficients are laid out in a format
described in Figure 13.41 . The coarse coefficients are placed towards the left side. For example, in
Example 13.7, we organized the DWT coefficient vector as

5
4

7
4

1 1

2 2 p

p

w 2 ðkÞ¼½c 0 ð 0 Þd 0 ð 0 Þd 1 ð 0 Þd 1 ð 1 Þ ¼

Let us look at the following simulation examples.