Smooth orthonormal wavelet libraries: design and application

For signal-based design of orthonormal (ON) wavelets, an optimization of a cost function over an N -dimensional angle space is required. However: (1) the N -dim space includes both smooth and non-smooth wavelets; (2) many of the smooth wavelets are similar in shape. A more practical approach for some applications may be to construct a library of smooth ON wavelets in advance—a library that consists of representative wavelet shapes for a given filter length. Existing ON wavelet libraries (Daubechies, nearlysymmetric, Coiflets) provide only one wavelet for each filter length. We construct ON wavelet libraries using local variation to determine wavelet smoothness and the discrete inner product to discriminate between wavelet shapes. The relationship between library size and the similarity threshold is investigated for various filter lengths. We apply an entropy-based wavelet selection algorithm to an example signal set, and investigate compactness in the wavelet domain as a function of library size.