Multiwavelet Frames in Signal Space Originated From Hermite Splines

We present a method for construction of multiwavelet frames for manipulation of discrete signals. The frames are generated by three-channel perfect reconstruction oversampled multifilter banks. The design of the multifilter bankstarts from a pair of interpolatory multifilters. We derive these interpolatory multifilters from the cubic Hermite splines. We use the original preprocessing algorithms, which transform scalar signals into vector arrays that serve as inputs to the oversampled analysis multifilter banks. These preprocessing algorithms do not degrade the approximation accuracy of the transforms of the vectors by multifilter banks. The postprocessing algorithms convert the vector output of the synthesis multifilter banks into scalar signal. The discrete framelets, generated by the designed filter banks, are symmetric and have short support. The analysis framelets have four vanishing moments, whereas the synthesis framelets converge to Hermite splines supported on the interval [-1,1]