Impedance matrix compression using an effective quadrature filter

An effective quadrature mirror filter (QMF) proposed by Vaidyanathan has be en used to solve 2D scattering problems. QMF has been popular for some time in digital signal processing, under the names of multirate sampling, wavel ets, etc. In this work, the impulse response coefficients of QMF were used to construct the wavelet transform matrix. Using the matrix to transform th e impedance matrices of 2D scatterers produces highly sparse moment matrice s that can be solved efficiently. Such a presentation provides better spars ity than the celebrated and widely used Daubechies wavelets. These QMF coef ficients are dependent on the filter parameters such as transition bandwidt h and filter length. It was found that the sharper the transition bandwidth , the greater the reduction in nonzero elements of the impedance matrix. It also can be applied in the wavelet packet algorithm to further sparsify th e impedance matrix. Numerical examples are given to demonstrate the effecti veness and validity of our finding.