Digital filter design by UL matrix decomposition

The direct transformation of hybrid or state equations of an analog network into a convenient matrix difference equation is described. This procedure effects a bilinear transformation of the original frequency variable s Into z without requiring transfer functions to be formed. An upper and lower decomposition of the new system matrix into UL triangular factors is introduced which provides a very economical numerical solution algorithm. This transformation procedure is applied to ladder filters to yield a new class of digital filters, related to the wave digital filter. A´low-pass digital filter realization is considered in detail, and it is noted that It lends itself to multiplexing.