Numerical solutions for orthogonal wavelet filters by Newton method

Abstract The wavelet transform has recently generated much interest in applied mathematics, signal processing and image coding. Mallat (1989) used the concept of the function space as a bridge to link the wavelet transform and multiresolution analysis. Daubechies (1990) added regularity conditions to find 2 N , 2⩽ N ⩽10, tap coefficients for orthogonal wavelet filters. Owing to the difficulty of finding their closed solutions for large N a numerical method called the Newton method is proposed. We constructed the orthogonal wavelet filter with 2 N -tap coefficients by N linear equations and N nonlinear equations. The 2 N -tap, 2⩽ N ⩽10, coefficients we found are very consistent with those of Daubechies. Also, the method can be used to find the orthogonal wavelet filter with N - tap coefficients for N >10.