Wavelet Toolbox

Wavelet Shapes

One-dimensional analysis is based on one scaling function and one wavelet . Two-dimensional analysis (on a square or rectangular grid) is based on one scaling function and three wavelets.

THe following figure shows and for each wavelet, except the Morlet wavelet and the Mexican hat, for which does not exist. All the functions decay quickly to zero. The Haar wavelet is the only noncontinuous function with three points of discontinuity (0, 0.5, 1). The functions oscillate more than associated functions. coif2 exhibits some angular points; db6 and sym6 are quite smooth. The Morlet and Mexican hat wavelets are symmetrical.

Figure 6-1 Various One-Dimensional Wavelets

Finer and Coarser Resolutions

Wavelets and Associated Families