On a choice of wavelet bases in the wavelet transform approach

摘要

The Daubechies orthogonal wavelet (DOW) is compared with the nonorthogonal cardinal spline wavelet (NCSW) in the wavelet transform approach and it is shown that the DOW is better than the NCSW in view of the computation cost. First, the computation cost required for the wavelet transform based on the DOW is less than that based on the NCSW because the DOW has smaller support provided the same number of vanishing moments of wavelets is used. Second, in contrast with the fact that the wavelet transform based on the DOW does not affect the condition number of the impedance matrix, that, based on the NCSW, has an effect to make it very large. As a result, even though the NCSW results in a sparser impedance matrix, it requires more computation cost for solving the resultant matrix equation in comparison with the DOW because the cost depends not only on the sparsity, but also on the condition number of the matrix.