Analysis of truncated periodic array using two-stage wavelet-packet transformations for impedance matrix compression

A novel method of moments procedure is applied to the problem of scattering by metallic truncated periodic arrays. In such problems, the induced current shows localized behavior within the unit cell and at the same time exhibits cell-to-cell periodicity. In order to select a set of expansion functions that may account for such behavior, a two-stage basis transformation, of which the first stage is an ordinary wavelet transformation performed independently on each unit-cell, has been applied to a pulse basis. The resultant basis functions at the first stage are regrouped and retransformed to reveal the periodicity of their coefficients. Expansion functions are then iteratively selected from this newly constructed basis to form a compressed impedance matrix. The compression ratios obtained in this manner are higher than the compression ratio achieved using a basis constructed via an ordinary single-stage wavelet transformation, where compression is the ratio between the number of nonzero elements in the matrix used to solve the problem and the number of elements in the original matrix. An even higher compression is attained by considering, in addition, functions that reveal array-end related features and iteratively selecting the expansion from an overcomplete dictionary.