Impedance matrix compression using effective quadrature filter

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Impedance matrix compression using effective quadrature filter

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An effective quadrature mirror filter (QMF) proposed by Vaidyanathan has been used to solve 2D scattering problems. QMF has been popular for some time in digital signal processing, under the names of multirate sampling, wavelets, etc. In this work, the impulse response coefficients of QMF were used to construct the wavelet transform matrix. Using the matrix to transform the impedance matrices of 2D scatterers produces highly sparse moment matrices that can be solved efficiently. Such a presentation provides better sparsity than the celebrated and widely used Daubechies wavelets. These QMF coefficients are dependent on the filter parameters such as transition bandwidth 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 the impedance matrix. Numerical examples are given to demonstrate the effectiveness and validity of our finding.

Inspec keywords: impedance matrix; sparse matrices; wavelet transforms; transient response; electromagnetic wave scattering; channel bank filters; quadrature mirror filters; lattice filters

Other keywords: wavelet transform matrix; 2D scattering problems; effective quadrature filter; filter parameters; impulse response coefficients; nonzero elements; quadrature mirror filter; wavelet packet algorithm; filter length; QMF coefficients; impedance matrix compression; sparsity; sparse moment matrices; transition bandwidth

Subjects: Integral transforms in numerical analysis; Electromagnetic wave propagation; Linear algebra (numerical analysis); Filtering methods in signal processing

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