Do Bounded Signals Have Bounded Amplitudes?

Multidimensional Systems and Signal Processing

Volumn 9, Issue 4, 1998, Pages 419-424

  Louqhlin, Patrick J ^a  

^a University of Pittsburgh   (United States)

Author keywords

Amplitude modulation; Analytic signal; Frequency modulation; Hilbert transform; Instantaneous amplitude; Instantaneous frequency

Indexed keywords

AMPLITUDE MODULATION; FREQUENCY MODULATION; MATHEMATICAL MODELS; MATHEMATICAL TRANSFORMATIONS;

HILBERT TRANSFORMS;

SIGNAL PROCESSING;

EID: 0032180511     PISSN: 09236082     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1008470710787     Document Type: Article

References (28)

1. E. Bedrosian, "A Product Theorem for Hilbert Transforms," Proc. IEEE, vol. 51, 1963, pp. 868-869.
2. J. Carson and T. Fry, "Variable Frequency Electric Circuit Theory with Application to the Theory of Frequency Modulation," Bell Syst. Tech. J., vol. 16, 1937 pp. 513-540.
3. T. Claasen and W. Mecklenbrauker, "The Wigner Distribution - A Tool for Time-Frequency Analysis (Parts I & III)" Phil. J. Res., vol. 35, 1980, pp. 217-250, pp. 372-389.
4. L. Cohen, "Distributions Concentrated Along the Instantaneous Frequency," SPIE vol. 1348 Adv. Sig. Proc. Algs., Architect. and Implement., 1990, pp. 149-157.
5. L. Cohen, "Instantaneous 'Anything'," IEEE Proc. ICASSP'93, vol. IV, 1993, pp. 105-108.
6. L. Cohen, Time-Frequency Analysis, Prentice-Hall, 1995, Ch. 2.
7. L. Cohen and C. Lee, "Instantaneous Frequency, Its Standard Deviation and Multicomponent Signals," SPIE vol. 975 Adv. Algs. and Architect, for Sig. Proc. III, 1988, pp. 186-208.
8. L. Cohen and T. Posch, "Positive Time-Frequency Distribution Functions," IEEE Trans. ASSP, vol. 33, 1985, pp. 31-37.
9. L. Cohen and Y. Zaparovanny, "Positive Quantum Joint Distributions," J. Math. Phys, vol. 21, no. 4, 1980, pp. 794-796.
10. L. Fink, "Relations Between the Spectrum and Instantaneous Frequency of a Signal" [English translation], Problemy Peredachi Informatsii, vol. 2, no. 4, 1966, pp. 26-38.
11. D. Gabor, "Theory of Communication," Jour. IEE, vol. 93, 1946, pp. 429-457.
12. M. Gupta, "Definition of Instantaneous Frequency and Frequency Measurability," Am. J. Phys., vol. 43, no. 12, 1975, pp. 1087-1088.
13. P. Loughlin and B. Tacer, "Comments on the Interpretation of Instantaneous Frequency," IEEE Sig. Proc. Lttrs., vol. 4, no. 5, 1997, pp. 123-125.
14. P. Loughlin and B. Tacer, "On the Amplitude- and Frequency-Modulation Decomposition of Signals," J. Acoust. Soc. Am., vol. 100, no. 3, 1996, pp. 1594-1601
15. P. Loughlin and B. Tacer, "Instantaneous Frequency and the Conditional Mean Frequency of a Signal," Signal Processing, vol. 60, 1997, pp. 153-162.
16. L. Mandel, "Interpretation of Instantaneous Frequencies," Am. J. Phys., vol. 42, 1974, pp. 840-846.
17. P. Maragos, J. Kaiser and T. Quatieri, "Energy Separation in Signal Modulations with Application to Speech Analysis," IEEE Trans. Sig. Proc., vol. 41, no. 10, 1993, pp. 3024-3051.
18. A. Nuttal, "On the Quadrature Approximation to the Hilbert Transform of Modulated Signals," Proc. IEEE, vol. 54, 1966, pp. 1458-1459.
19. B. Picinbono, "On Instantaneous Amplitude and Phase of Signals," IEEE Trans. Sig. Proc., vol. 45, no. 3, 1997, pp. 552-560.
20. A. Rihaczek, "Hilbert Transforms and the Complex Representation of Real Signals," Proc. IEEE, vol. 54, 1966, pp. 434-435.
21. J. Shekel, "'Instantaneous' Frequency," Proc. IRE, 1953, p. 548.
22. A. Smolinski, "On the Hilbert Envelope of a High Frequency Pulse," [English translation], Bulletin De L'Academie Polonaise Des Sciences, vol. XIX, no. 6, 1971.
23. D. Vakman, "On the Definition of Concepts of Amplitude, Phase and Instantaneous Frequency of a Signal," Trans. Radio Eng. and Electron. Phy., 1972, pp. 754-759.
24. D. Vakman, "Do We Know What are the Instantaneous Frequency and Instantaneous Amplitude of a Signal?," Trans. Radio Eng. and Electron. Phy., vol. 21, 1976, pp. 95-100.
25. D. Vakman, "On the Analytic Signal, the Teager-Kaiser Energy Algorithm, and Other Methods for Defining Amplitude and Frequency," IEEE Trans. Sig. Proc., vol. 44, no. 4, 1996, pp. 791-797.
26. D. Vakman and L. Vainshtein, "Amplitude, Phase, Frequency - Fundamental Concepts of Oscillation Theory," [English translation], Sov. Phys. Usp., vol. 20, no. 12, 1977.
27. B. Van der Pol, "The Fundamental Principles of Frequency Modulation," J. IEE, vol. 93, 1946, pp. 153-158.
28. J. Ville, "Theorie et Applications de la Notion de Signal Analytique," Cables et Transmissions, vol. 2A, no. 1, 1948, pp. 61-74. [English translation by RAND Corp., Tech. Rep. T-92, Santa Monica, CA, 1958.]