An application of wavelet bases in the spectral domain analysis of transmission line discontinuities

Abstract

The local support and vanishing moment property of wavelet bases have been recently used to obtain a sparse matrix representation of integral equations in the spatial domain. In this paper, an application of the cubic spline and the corresponding semi-orthogonal wavelets in the spectral domain is proposed for the evaluation of the reflection coefficient for open/short transmission lines. Because of the nearly optimal time (space)–frequency (wavenumber)–window product of the cubic spline and wavelet, the double spectral integrals appearing in the formulation can be computed more efficiently than with the commonly used piecewise sinusoidal (PWS) or triangular basis functions. It is shown that the time–frequency-window product of the triangular and PWS function are close to each other, whereas those of the cubic spline/wavelet are close to 0·5, the lowest possible value corresponding to functions of Gaussian class. Both the PWS and wavelet bases are applied to microstrip and coplanar waveguides with isotropic and anisotropic substrates, and the results are compared with published theoretical and experimental data. It is observed that even though the number of splines/wavelets required for an accurate representation of the current distribution in the transmission line is almost twice as high as the number of PWS functions, the overall computation time decreases significantly in the former case. © 1998 John Wiley & Sons, Ltd.