Spectral Transformations - Biomedical Signal Analysis: Contemporary Methods and Applications - page 57

c(1,n)

2

2 h 0 (-n)

c(0,n)

d(1,n)

2

2 h 1 (-n)

Figure 2.12
First level of the multiscale signal decomposition.

c 1,n = √ 2 h 0 ( k − 2 n ) c 0,k (2.72)

and

d 1,n = √ 2 h 1 ( k − 2 n ) c 0,k (2.73)

These last two analysis equations relate the DWT coecients at a finer
scale to the DWT coecients at a coarser scale. The analysis operations
are similar to ordinary convolution. The similarity between ordinary
convolution and the analysis equations suggests that the scaling function
coecients and wavelet function coecients may be viewed as impulse
responses of filters. In fact, the set can be viewed as

a paraunitary FIR filter pair. Figure 2.12 illustrates this.
The discrete signal d 1,n is the WT coecient the resolution 1 / 2and
describes the detail signal or difference between the original signal c 0,n
and its smooth undersampled approximation c 1,n .
For m = 2, we obtain at the resolution 1/4 the coecients of the

{ h 0 ( − n ) ,h 1 ( − n ) }