Spectral Transformations - Biomedical Signal Analysis: Contemporary Methods and Applications - page 58

c(2, n)

2

2 h 0 (-n)

Res 1/4

c(1,n)
Res 1/2

2

2 h 0 (-n)

Low-pass d(2, n)

c(0,n)

2

2 h 1 (-n)

Res 1/4

Res 1

d(1,n)

2

2 h 1 (-n)

Res 1/2

High-pass

Figure 2.13
Multiscale pyramid decomposition.

smoothed signal (approximation) and the detail signal (approximation
error) as

c 2,n = √ 2 c 1,k h 0 ( k − 2 n ) (2.74)

d 2,n = √ 2 c 1,k h 1 ( k − 2 n ) (2.75)

These relationships are illustrated in the two-level multiscale pyramid
in figure 2.13.
Wavelet synthesis is the process of recombining the components of
a signal to reconstruct the original signal. The inverse discrete wavelet
transformation, or IDWT, performs this operation. To obtain c 0,n ,the
terms c 1,n and d 1,n are upsampled and convoluted with the filters h 0 ( n )
and h 1 ( n ), as shown in figure 2.14.
The results of the multiscale decomposition and reconstruction of a
dyadic subband tree are shown in figure 2.15 and describe the analysis
and synthesis part of a two-band PR-QMF bank.
It is important to note that the recursive algorithms for decompo-
sition and reconstruction can easily be extended for a two-dimensional
signal (image) [278] and play an important role in image compression.