Title :
Time-frequency transfer function and realization algorithm for discrete periodic linear systems
Author :
Park, Peter B. ; Verriest, Erik I.
Author_Institution :
IBM Federal Syst. Co., Rockville, MD, USA
Abstract :
A realization of a linear periodically time-varying system of order n with m inputs, p outputs and period N is given by x(k+1)=A[/k]x(k)+Bsub [/k]u(k), y(k)=C[/k]x(k)+Dsub [/k]u(k), Where [k] = k mod N. The parameters of the realization are denoted by ((Ak, Bk , Ck, Dk))N. The construction of a state variable representation, from a given pulse response, is outlined. Time-frequency analysis/synthesis transfer function are defined by means of proper z-transforms of the pulse response h(l,r), and their N-phase decomposition is introduced. The realisation problem is reduced to solving the matrix equation He(z)=Ce(zI-Ae )-1Be+De where He(z) is the extended matrix transfer function constructed from h(l,r) through the N-phase decomposition F(l,z) or G(z,r)
Keywords :
Z transforms; discrete systems; linear systems; matrix algebra; time-frequency analysis; time-varying systems; transfer functions; decomposition; discrete periodic linear systems; linear periodically time-varying system; matrix transfer function; pulse response; state variable representation; time-frequency transfer function; z-transforms; Chromium; Equations; Linear systems; Matrix decomposition; Polynomials; Problem-solving; Pulse generation; Time frequency analysis; Time varying systems; Transfer functions;
Conference_Titel :
Decision and Control, 1993., Proceedings of the 32nd IEEE Conference on
Conference_Location :
San Antonio, TX
Print_ISBN :
0-7803-1298-8
DOI :
10.1109/CDC.1993.325627