A Digital Signal Processing Perspective on Numerical Methods for Circuit Simulation

摘要

This work explores the relationship between digital signal processing theory and the numerical methods for circuit simulation. It is shown that by using B-spline basis function as the interpolation function, a fast recursive filtering approach can be derived for solving the ordinary differential equations. Since the spline function can be used as the scaling function in wavelet decomposition and reconstruction, the proposed method provides an alternative approach to the recently proposed wavelet collocation method for circuit simulation. Instead of decomposing the solutions directly into the wavelet basis functions at all levels and solving the obtained linear equations as in the wavelet collocation method, the proposed approach applies the multiresolution analysis. Specifically, first the expansion coefficients with respect to the scaling spline basis functions at the highest resolution level are obtained using the fast recursive filtering approach, then the wavelet coefficients at all levels are obtained by applying the fast wavelet decomposition algorithm. The experimental results show that the proposed approach is very promising.