Time-frequency transfer function calculus (symbolic calculus) of linear time-varying systems (linear operators) based on a generalized underspread theory

Journal of Mathematical Physics

Volumn 39, Issue 8, 1998, Pages 4041-4070

  Matz, Gerald ^a   Hlawatsch, Franz ^a  

^a VIENNA UNIVERSITY OF TECHNOLOGY   (Austria)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032369145     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.532495     Document Type: Article

References (119)

1. E. P. Wigner, Phys. Rev. 40, 749 (1932).
2. J. E. Moyal, Proc. Cambridge Philos. Soc. 45, 99 (1949).
3. E. P. Wigner, in Perspectives in Quantum Theory, edited by W. Yourgrau and A. van der Merwe (Dover. New York, 1971), Vol. 40, Chap. 4, pp. 25-36.
4. N. G. de Bruijn, Nieuw Archief voor Wiskunde (3) XXI, 205 (1973).
5. J. Ville, Cables Transm. 2eA., No. 1, 61 (1948).
6. T. A. C. M. Claasen and W. F. G. Mecklenbräuker, Philips J. Res. 35, 217 (1980).
7. T. A. C. M. Claasen and W. F. G. Mecklenbrauker, Philips J. Res. 35, 372 (1980).
8. The Wigner Distribution - Theory and Applications in Signal Processing, edited by W. Mecklenbräuker and F. Hlawatsch (Elsevier, Amsterdam, 1997).
9. P. Flandrin, Temps-Fréquence (Hermès, Paris, 1993).
10. A. Messiah, Quantum Mechanics (North-Holland, Amsterdam, 1965), Vol. I.
11. G. B. Folland and A. Sitaram. J. Fourier Anal. Appl. 3, 207 (1997).
12. D. Gabor, J. IEE 93, 429 (1946).
13. N. G. de Bruijn, in Inequalities, edited by O. Shisha (Academic, New York, 1967), pp. 57-71.
14. C. L. Fefferman, Bull. Am. Math. Soc. 9, 129 (1983).
15. G. B. Folland, Harmonic Analysis in Phase Space. Vol. 122 of Annals of Mathematics Studies (Princeton University Press, Princeton, NJ, 1989).
16. A. Perelomov, Generalized Coherent States and Their Applications (Springer-Verlag, Berlin, 1986).
17. I. Daubechies, IEEE Trans. Inf. Theory 34, 605 (1988).
18. S. T. Ali, J.-P. Antoine, J.-P. Gazeau, and U. A. Müller, Rev. Math. Phys. 7/7, 1013 (1995).
19. Gabor Analysis and Algorithms: Theory and Applications, edited by H. G. Feichtinger and T. Strohmer (Birkhäuser, Boston, 1998).
20. R. Tolimieri and M. An, Time-Frequency Representations (Birkhäuser, Boston, 1998).
21. F. Hlawatsch and G. F. Boudreaux-Bartels, IEEE Signal Process. Mag. 9, 21 (1992).
22. S. H. Nawab and T. F. Quatieri, in Advanced Topics in Signal Processing, edited by J. S. Lim and A. V. Oppenheim (Prentice-Hall, Englewood Cliffs, NJ, 1988). Chap. 6, pp. 289-337.
23. R. E. Crochiere and L. R. Rabiner, Multirate Digital Signal Processing (Prentice-Hall, Englewood Cliffs, NJ, 1983).
24. M. R. Portnoff, IEEE Trans. Acoust., Speech, Signal Process. 28, 55 (1980).
25. J. Zak, Phys. Rev. Lett. 19, 1385 (1967).
26. A. J. E. M. Janssen, Philips J. Res. 43, 23 (1988).
27. H. Bölcskei and F. Hlawatsch, IEEE Trans. Signal Process. 45, 851 (1997).
28. M. G. Bellanger, G. Bonnerot, and M. Coudreuse, IEEE Trans. Acoust., Speech, Signal Process. 24, 109 (1976).
29. P. P. Vaidyanathan, Multirate Systems and Filter Banks (Prentice-Hall, Englewood Cliffs, NJ. 1993).
30. M. Vetterli and J. Kovačević, Wavelets and Subband Coding (Prentice-Hall, Englewood Cliffs, NJ, 1995).
31. N. L. Balazs and B. K. Jennings, Phys. Rep. 104, 347 (1984).
32. H. Weyl, The Theory of Groups and Quantum Mechanics (Dover, New York, 1950).
33. J. C. T. Pool, J. Math. Phys. 7, 66 (1966).
34. L. Cohen, J. Math. Phys. 7, 781 (1966).
35. L. Cohen, J. Math. Phys. 17, 1863 (1976).
36. C. L. Mehta, J. Math. Phys. 5, 677 (1964).
37. J. J. Kohn and L. Nirenberg, Commun. Pure Appl. Math. 18, 269 (1965).
38. A. Grossmann, G. Loupias, and E. M. Stein, Ann. Inst. Fourier 18, 343 (1968).
39. A. Voros, Ann. Inst. Henri Poincaré 26, 343 (1977).
40. L. Hörmander, Commun. Pure Appl. Math. 32, 359 (1979).
41. R. Howe, J. Funct. Anal. 38, 188 (1980).
42. W. Kozek, Ph.D. thesis, Vienna University of Technology, 1997.
43. W. Kozek, IEEE Trans. Signal Process. 45, 219 (1997).
44. W. Kozek, in Gabor Analysis and Algorithms: Theory and Applications, edited by H. G. Feichtinger and T. Strohmer (Birkhäuser, Boston, 1998), Chap. 10, pp. 323-352.
45. R. Bourdier, J. F. Allard, and K. Trumpf. Signal Process. 15, 193 (1988).
46. W. Kozek and F. Hlawatsch, in Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis (Victoria, B.C., Canada, 1992), pp. 163-166.
47. A. M. Sayeed, P. Lander, and D. L. Jones. J. Electrocardiol. 28, 53 (1995).
48. G. W. Wornell, IEEE Trans. Inf. Theory 41, 1418 (1995).
49. G. W. Wornell, IEEE Trans. Inf. Theory 42, 488 (1996).
50. A. A. Beex and M. Xie, Proceedings of the IEEE ICASSP-95, Detroit, MI. 1995, pp. 1565-1568.
51. H. Kirchauer, F. Hlawatsch, and W. Kozek, in Ref. 50, pp. 1549-1552.
52. G. Matz and F. Hlawatsch, in Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis (Paris, France, 1996), pp. 213-216.
53. J. A. Sills, Ph.D. thesis, Georgia Institute of Technology, Atlanta, 1995.
54. G. Matz, F. Hlawatsch, and W. Kozek, IEEE Trans. Signal Process. 45, 1520 (1997).
55. W. Kozek, F. Hlawatsch, H. Kirchauer, and U. Trautwein, Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis, Philadelphia, PA. 1994, pp. 417-420.
56. A. Voros, J. Funct. Anal. 29, 104 (1978).
57. A. Messiah, Quantum Mechanics (North-Holland, Amsterdam, 1965), Vol. II.
58. T. Arai, J. Math. Phys. 36, 622 (1995).
59. A. W. Naylor and G. R. Sell, Linear Operator Theory in Engineering and Science, 2nd ed. (Springer-Verlag, New York, 1982).
60. I. M. Gelfand and G. E. Schilow, Verallgemeinerte Funktionen (Distributionen) (VEB, Berlin, 1960).
61. I. C. Gohberg and M. G. Krein, Introduction to the Theory of Linear Nonselfadjoint Operators (American Mathematical Society, Providence, RI, 1969).
62. L. A. Zadeh, Proc. IRE 76, 291 (1950).
63. P. A. Bello, IEEE Trans. Commun. Syst. 11, 360 (1963).
64. R. G. Shenoy and T. W. Parks, IEEE Trans. Signal Process. 42, 318 (1994).
65. A. J. E. M. Janssen, Philips J. Res. 44, 7 (1989).
66. H. Weyl, Z. Phys. 46, 1 (1928).
67. W. Kozek, Signal Process. 29, 77 (1992).
68. W Kozek, in Ref. 46, pp. 167-170.
69. P. Flandrin, B. Escudié, and J. Gréa, C. R. Acad. Sci. Paris, Ser. I 294, 281 (1982).
70. A. J. E. M. Janssen, Philips J. Res. 37, 79 (1982).
71. F. Hlawatsch and P. Flandrin, in The Wigner Distribution - Theory and Applications in Signal Processing, edited by W. Mecklenbräuker and F. Hlawatsch (Elsevier, Amsterdam, 1997), pp. 59-133.
72. A. W. Rihaczek, IEEE Trans. Inf. Theory 14, 369 (1968).
73. R. Simon, E. C. G. Sudarshan, and N. Mukunda, Phys. Rev. A 36, 3868 (1987).
74. A. Weil, Acta Math. 111, 143 (1964).
75. W. Miller, Jr., in Radar and Sonar, Part I, edited by R. E. Blahut, W. Miller, Jr., and C. H. Wilcox (Springer-Verlag, New York, 1991), pp. 66-168.
76. T. Kailath, IEEE Trans. Inf. Theory 9, 233 (1963).
77. T.-Y. Leou and J. K. Aggarwal, Proc. IEEE 72, 980 (1984).
78. J. G. Proakis, Digital Communications, 3rd ed. (McGraw-Hill, New York, 1995).
79. J. A. Sills and E. W. Kamen, Circuits Syst. Signal Process. 15, 609 (1996).
80. S. G. Mallat, G. Papanicolaou, and Z. Zhang, Ann. Stat. 26, 1 (1998).
81. K. A. Sostrand, Proc. NATO Adv. Study Inst. Signal Process. Emphasis Underwater Acoust. 2, 25.1 (1968).
82. R. Howe, Bull. Am. Math. Soc. 3, 821 (1980).
83. K. E. Cahill and R. J. Glauber, Phys. Rev. 177, 1882 (1969).
84. R. S. Kennedy, Fading Dispersive Communication Channels (Wiley, New York, 1969).
85. H. L. Van Trees, Detection, Estimation, and Modulation Theory, Part III: Radar-Sonar Signal Processing and Gaussian Signals in Noise (Krieger, Malabar, 1992).
86. P. Flandrin, in Time and Frequency Representation of Signals and Systems, edited by G. Longo and B. Picinbono (Springer, Wien, 1989), pp. 69-124.
87. G. Matz, Ph.D. thesis, Vienna University of Technology, in preparation.
88. R. Estrada, J. M. Gracia-Bondía, and J. C. Várilly, J. Math. Phys. 30, 2789 (1989).
89. F. Bayen, M. Flato, C Fronsdal, et al., Ann. Phys. 111, 61 (1978).
90. W. Martin and P. Flandrin, IEEE Trans. Acoust., Speech, Signal Process. 33, 1461 (1985).
91. M. B. Priestley, J. R. Stat. Soc. Ser. B 27, 204 (1965).
92. F. Hlawatsch, Proceedings of the IEEE ISCAS-92, San Diego, CA. 1992, pp. 1459-1462.
93. M. Sandell, Ph.D. thesis, Lulea University of Technology, Lulea, Sweden, 1996.
94. R. Haas and J. C. Belliore, Wireless Personal Commun. 5, 1 (1997).
95. W. Kozek and A. F. Molisch, Proceedings of the IEEE Workshop on Signal Processing Applications in Wireless Communication (Paris, France, 1997), pp. 325-328.
96. W. Kozek and A. F. Molisch, IEEE J. Sel. Areas Comm. (submitted).
97. A Córdoba and C. Fefferman, Comm. Partial Diff. Eqns. 3, 979 (1978).
98. R. Rochberg, Lecture Notes Pure Appl. Math. 51, 425 (1990).
99. Y. Meyer, in AMS Proceedings of the Symposia in Applied Mathematics: Different Perspectives on Wavelets, edited by I. Daubechies (AMS, Providence, RI, 1993), pp. 35-58.
100. F. Hlawatsch, IEEE Trans. Signal Process. 39, 1564 (1991).
101. P. M. Woodward, Probability and Information Theory with Application to Radar (Pergamon, London, 1953).
102. A. Papoulis, Signal Analysis (McGraw-Hill, Singapore, 1984).
103. C. H. Wilcox, in Radar and Sonar, Part I, edited by R. E. Blahut, W. Miller, Jr., and C. H. Wilcox (Springer-Verlag, New York, 1991), pp. 229-260.
104. R. J. Glauber, Phys. Rev. 131, 2766 (1963).
105. A. Dembo and D. Malah, IEEE Trans. Acoust., Speech, Signal Process. 36, 168 (1988).
106. W. Kozek, H. G. Feichtinger, and J. Scharinger, Proceedings of the IEEE ISCAS-96, Atlanta, GA, 1996, pp. 509-512.
107. H. G. Feichtinger and K. Gröchenig, in Wavelets - A Tutorial in Theory and Applications, edited by C. Chui (Academic, Boston, 1992), pp. 359-397.
108. S. Farkash and S. Raz, IEEE Trans. Signal Process. 42, 611 (1994).
109. K. Swaminathan and P. P. Vaidyanathan, IEEE Trans. Circuits Syst. 33, 1170 (1986).
110. M. Vetterli, IEEE Trans. Acoust., Speech, Signal Process. 35, 356 (1987).
111. M. Poize, M. Renaudin, and P. Venier, Quatorzième Colloque GRETSI (Juan-Les-Pins, France, 1993), pp. 351-354.
112. Y. Lin and P. P. Vaidyanathan, Proceedings of the APCCAS-94 (Taipei, Taiwan, 1994), pp. 254-259.
113. H. Bölcskei, F. Hlawatsch, and H. G. Feichtinger, in Proceedings of the IEEE ICASSP-96, Atlanta, GA, 1996, Vol. 3, pp. 1391-1394.
114. H. Bölcskei and F. Hlawatsch, in Gabor Analysis and Algorithms: Theory and Applications, edited by H. G. Feichtinger and T. Strohmer (Birkhäuser, Boston, 1998), Chap. 9, pp. 295-322.
115. K. Nowak, Colloq. Math. LXV, Fasc. 1, 149 (1993)
116. A. Papoulis, Probability, Random Variables, and Stochastic Processes, 3rd ed. (McGraw-Hill, New York, 1991).
117. P. Flandrin and W. Martin, in The Wigner Distribution - Theory and Applications in Signal Processing, edited by W. Mecklenbräuker and F. Hlawatsch (Elsevier, Amsterdam, 1997). pp. 211-267.
118. A. Calderón and R. Vaillancourt, J. Math. Soc. Jpn. 23, 374 (1971).
119. F. A. Berezin, Math. USSR Sb. 15, 577 (1971).