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 2N, 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 2N-tap coefficients by N linear equations and N nonlinear equations. The 2N-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.[[fileno]]2030206010044[[department]]資訊工程學