Product of second moments in time and frequency for discrete-time signals and the uncertainty limit

Signal Processing

Volumn 67, Issue 1, 1998, Pages 59-76

  Doroslovački, Miloš I ^a  

^a George Washington University   (United States)

Author keywords

Discrete time signals; Energy distributions; Second moments; Time frequency localization; Uncertainty relations

Indexed keywords

SAMPLED DATA CONTROL SYSTEMS; SPECTRUM ANALYSIS; SPURIOUS SIGNAL NOISE;

UNCERTAINTY LIMIT;

SIGNAL PROCESSING;

EID: 0032072984     PISSN: 01651684     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0165-1684(98)00022-X     Document Type: Article

References (14)

1. P. Billingsley, Probability and Measure, 2nd ed., Wiley, New York, 1986.
2. I.N. Bronshtein, K.A. Semendyaev, 10th ed., Spravochnik po Matematike, Nauka, Moscow, 1964 (in Russian).
3. L.C. Calvez, P. Vilbé, On the uncertainty principle in discrete-signals, IEEE Trans. Circuits Systems II 39 (6) (June 1992) 394-395.
4. M. Doroslovački, Discrete-time signals and uncertainty relations involving ordinary second moments in time and frequency, Proc. IEEE-SP Internat. Symp. Time-Frequency, Time-Scale Analysis, Philadelphia, PA, October 1994, pp. 186-189.
5. M. Doroslovački, H. Fan, Generalized Heisenberg's uncertainty relation for signals, Proc. Conf. Inform. Sci. Syst., Baltimore, MD, March 1993, pp. 464-469.
6. W. Feller, An Introduction to Probability Theory and Its Applications, 3rd ed., Vol. 1, Wiley, New York, 1968.
7. D. Gabor, Theory of communications, J. IEE (London), 93 (III) (November 1946) 429-457.
8. R. Ishii, K. Furukawa, The uncertainty principle in discrete signals, IEEE Trans. Circuits Systems 33 (10) (October 1986) 1032-1034.
9. D.S. Mitrinović, Introduction to Special Functions, 2nd ed., Gradjevinska Knjiga, Belgrade, 1975 (in Serbo-Croat).
10. A.V. Oppenheim, R.W. Schafer, Digital Signal Processing, Prentice-Hall, Englewood Cliffs, NJ, 1975.
11. A. Papoulis, Probability, Random Variables, and Stochastic Processes, McGraw-Hill, New York, 1965.
12. A. Papoulis, Signal Analysis, McGraw-Hill, New York, 1977.
13. E.D. Rainville, Special Functions, The Macmillan Company, New York, 1960.
14. H.L. Royden, Real Analysis, 3rd ed., Macmillan Publishing Company, New York, 1988.