Extending the transfer function calculus of time-varying linear systems: a generalized underspread theory

We extend the approximate transfer function calculus of "underspread" linear time-varying (LTV) systems introduced by W. Kozek (1992). Our extension is based on a new, generalized definition of underspread LTV systems that does not assume finite support of the systems' spreading function. We establish explicit bounds on various error quantities associated with the transfer function approximation. Our results yield a simple and convenient transfer function calculus for a significantly wider and practically more relevant class of LTV systems than that previously considered.

[1]  G. Folland.  Harmonic analysis in phase space , 1989 .

[2]  W. Kozek,et al.  Time-frequency signal processing based on the Wigner-Weyl framework , 1992, Signal Process..

[3]  Thomas W. Parks,et al.  The Weyl correspondence and time-frequency analysis , 1994, IEEE Trans. Signal Process..

[4]  Patrick Flandrin,et al.  Time-Frequency/Time-Scale Analysis , 1998 .

[5]  F. Hlawatsch,et al.  Linear and quadratic time-frequency signal representations , 1992, IEEE Signal Processing Magazine.

[6]  L. Zadeh,et al.  Frequency Analysis of Variable Networks , 1950, Proceedings of the IRE.

[7]  Ajem Guido Janssen,et al.  Wigner weight functions and Weyl symbols of non-negative definite linear operators , 1989 .

[8]  Joseph J. Kohn,et al.  An algebra of pseudo‐differential operators , 1965 .

[9]  W. Kozek,et al.  On the generalized Weyl correspondence and its application to time-frequency analysis of linear time-varying systems , 1992, [1992] Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis.

[10]  Franz Hlawatsch,et al.  Duality and classification of bilinear time-frequency signal representations , 1991, IEEE Trans. Signal Process..

[11]  Werner Kozek,et al.  On the transfer function calculus for underspread LTV channels , 1997, IEEE Trans. Signal Process..

[12]  Johannes Sj,et al.  AN ALGEBRA OF PSEUDODIFFERENTIAL OPERATORS , 1994 .

[13]  P. Bello.  Characterization of Randomly Time-Variant Linear Channels , 1963 .

[14]  Arch W. Naylor,et al.  Linear Operator Theory in Engineering and Science , 1971 .

[15]  Johannes Sjöstrand.  An algebra of pseudodifferential operators , 1994 .

[16]  A. Voros,et al.  An algebra of pseudodifferential operators and the asymptotics of quantum mechanics , 1978 .