Smooth, Compactly Supported Wavelets
David F. Walnut · Applied and numerical harmonic analysis · 2004
We have seen in Chapter 7 several examples of orthonormal wavelet bases. However, the only example we have seen so far of a compactly supported wavelet has been the Haar wavelet. In Section 5.4.1, we saw that the compact support of the Haar wavelets meant that the Haar decomposition had good time localization. Specifically, this meant that the Haar coefficients were effective for locating jump discontinuities and also for the efficient representation of signals with small support. We have also seen disadvantages in the fact that the Haar wavelets have jump discontinuities, specifically in the poorly decaying Haar coefficients of smooth functions (Section 5.4.3) and in the blockiness of images reconstructed from subsets of the Haar coefficients (Section 6.3.1).