Sparse matrix algorithm for digital filter analysis

When a computer is used to analyze a digital filter, a nodal analysis is applied to obtain a system transfer function. While other approaches have been used in the past, the sparse matrix technique is the most efficient for solving the nodal matrix equations. This project focuses upon the sparse matrix technique described by Wasniewski, et al, [2]. The two computer programs listed in the appendices, GAUSS and SPARSE, are compared to each other by means of a series of examples, The first GAUSS, uses the well-known Gaussian elimination method, and the second SPARSE, uses the sparse matrix technique for solving the nodal matrix equations. The results indicate that the SPARSE program requires less computer memory and computation time. Finally, three digital filter examples are presented in this paper. Each is tested with the computer programs SPARSE and GAUSS, and the output presented consists of plots of the three basic frequency responses of each filter example – magnitude in decibels, phase in radians, and group delay in samples.