Time-frequency synthesis of statistically matched Weyl-Heisenberg prototype signals

The use of a family of time-frequency shifted versions of a prototype signal, namely Weyl-Heisenberg (WH) sets, is a common feature of various concepts in signal analysis, processing and digital communication. The authors discuss the matching of WH prototype signals to important nonstationary environments. The statistical window optimization for the STFT/Gabor expansion of nonstationary processes is shown to be formally equivalent to optimal signal design for narrowband WSSUS channels. For the case of underspread channels/processes the authors derive approximate solutions to the optimization problem.<<ETX>>

[1]  W. Kozek,et al.  Correlative time-frequency analysis and classification of nonstationary random processes , 1994, Proceedings of IEEE-SP International Symposium on Time- Frequency and Time-Scale Analysis.

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

[3]  Steven M. Sussman,et al.  Least-square synthesis of radar ambiguity functions , 1962, IRE Trans. Inf. Theory.

[4]  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.

[5]  Calvin H. Wilcox,et al.  The Synthesis Problem for Radar Ambiguity Functions , 1991 .

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

[7]  Ingrid Daubechies,et al.  The wavelet transform, time-frequency localization and signal analysis , 1990, IEEE Trans. Inf. Theory.

[8]  A. Papoulis.  Signal Analysis , 1977 .

[9]  R. Tolimieri,et al.  Characterization of Weyl-Heisenberg frames via Poisson summation relationships , 1992, [Proceedings] ICASSP-92: 1992 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[10]  W. Kozek,et al.  Matched generalized Gabor expansion of nonstationary processes , 1993, Proceedings of 27th Asilomar Conference on Signals, Systems and Computers.