Pattern Recognition, 4th Edition

6.13. Discrete Time Wavelet Transform (DTWT)

The goal of this section is twofold. We first free ourselves from the Haar functions, and we seek the possibility of using other filters in place of H⁰,H¹. There is more than one reason for this generalization. An obvious reason is that the frequency responses of the Haar filters are far from ideal. If our aim is to split the original sequence into a hierarchy of “coarse” and “detailed” versions, we should require the filters that perform the splitting to be as close as possible to the ideal low/high-pass ones (Figure 6.15). Our next concern in this section is the inversion problem. That is, if we know the lower resolution versions, can we obtain the original sequence, x(n), as was the case with ...