Recursive synthesis of linear time-variant digital filters via Chebyshev approximation. (English) Zbl 0559.93037
In the paper the recursive realization of a generalized transfer function (GTF) as a linear time-variant (LTV) system is discussed. The GTF considered here is exactly the digital equivalent of the Zadeh independance for continuous-time linear time-variant systems. First, a recurrent equation relating the GTF and the coefficients of the time difference equation (TDE) is derived. To apply it, initial conditions for the GTF must be given. Then a system of equations giving the coefficients of TDE is obtained. For the case when the denominator of the GTF has the coefficients independent of the time, a canonical structure of implementing the GTF as a system is given. For general GTF the system of equations is overdetermined. In this case, by use of the Chebyshev norm, a ”best” solution is obtained. Finally, a numerical example is presented. We think the paper is a valuable contribution of digital LTV systems.
Reviewer: D.Stanomir
MSC:
93B50 | Synthesis problems |
93C55 | Discrete-time control/observation systems |
93E11 | Filtering in stochastic control theory |
41A50 | Best approximation, Chebyshev systems |
60G35 | Signal detection and filtering (aspects of stochastic processes) |
93C05 | Linear systems in control theory |
93C99 | Model systems in control theory |
93C57 | Sampled-data control/observation systems |