Optimized orthonormal wavelet filters with improved frequency separation

This paper proposes an optimization-based method to design orthonormal wavelet filters with improved frequency separation. The proposed approach adopts a parameterization of orthogonal filter banks which ensures that the resulting wavelets have at least two vanishing moments. The filter parameters are adjusted by a numerical optimization algorithm in order to minimize a cost function associated to cut-off sharpness. In comparison with standard orthonormal filters, the proposed method is shown to provide better trade-off between frequency selectivity and time resolution. For illustration, the optimized filters are employed in an application example involving the use of a wavelet-packet system identification scheme. As a result, the identification errors are smaller than those obtained by using a non-optimized filter with the same length.