Systolic computation of multivariable frequency response

Abstract

An algorithm intended for software implementation on a programmable systolic/wavefront computer is presented for the computation of a complex-valued frequency-response matrix G. Typically, real-valued state-space model matrices are given and the calculation of G must be performed for a very large number of values of the scalar frequency parameter. The algorithm is an orthogonal version of an algorithm described previously by A.J. Laub (ibid., vol.26, no.4, p.407-8, 1981). The system matrix A is reduced initially to an upper Hessenberg form which is preserved as the frequency varies subsequently. A systolic QR factorization of a certain complex-valued matrix is then implemented for effecting the necessary linear system solution (inversion). The critical computational component is the back solve. This computational component's process dependency graph is embedded optimally in space and time through the use of a nonlinear spacetime transformation. The computational period of the algorithm is O(n) where n is the order of the matrix A. >