Instantaneous frequency estimation when the amplitude is a stochastic process using stochastic calculus and bootstrapping

Circuits, Systems, and Signal Processing

Volumn 24, Issue 1, 2005, Pages 35-52

  Abutaleb, A ^a,b  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^b CAIRO UNIVERSITY   (Egypt)

Author keywords

Bootstrapping; Girsanov theory; Instantaneous frequency estimation; Ito calculus; Wigner Ville distribution

Indexed keywords

ALGORITHMS; COMPUTER SIMULATION; DIFFERENTIAL EQUATIONS; FREQUENCIES; MAXIMUM LIKELIHOOD ESTIMATION; POLYNOMIALS; RANDOM PROCESSES; SIGNAL TO NOISE RATIO;

BOOTSTRAPPING; GIRSANOV THEORY; INSTANTANEOUS FREQUENCY ESTIMATION; ITO CALCULUS; WIGNER-VILLE DISTRIBUTION;

SIGNAL PROCESSING;

EID: 17444403926     PISSN: 0278081X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00034-004-3081-9     Document Type: Article

References (28)

1. A. Abutaleb, 1997, A genetic algorithm for the maximum likelihood estimation of the parameters of sinusoids in noisy environment, Circuits Systems Signal Process., vol. 16, no. 1, pp. 69-81.
2. A. Abutaleb, 2002, Number theory and bootstrapping for phase unwrapping, IEEE Trans. Circuits and Systems Part I, vol. 49, no. 5, pp. 632-638.
3. B. Barkat, 2001, Instantaneous frequency estimation of nonlinear frequency modulated signals in the presence of multiplicative and additive noise, IEEE Trans. Signal Process., vol. 49, no. 10, pp. 2214-2222.
4. M. Benidir and A. Ouldali, 1999, Polynomial phase signal analysis based on the polynomial derivatives decomposition, IEEE Trans. Signal Process., vol. 47, no. 7, pp. 1954-1965.
5. J. Blackledge, 1989, Quantitative Coherent Imaging, Academic Press, London.
6. B. Boashash, 1992, Estimating and interpreting the instantaneous frequency of a signal, Proc. IEEE, vol. 80, no. 4, pp. 520-568.
7. B. Boashash, 2003, Time Frequency Analysis, Elsevier-Science, New York.
8. V. Chen and H. Ling, 2002, Time-Frequency Transforms for Radar Imaging and Signal Analysis, Artech House, Boston.
9. B. Efron and R. Tibshirani, 1994, An Introduction to the Bootstrap Chapman & Hall, New York.
10. D. Ghiglia and M. Pritt, 1998, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software, John Wiley, New York.
11. R. Goldstein, H. Zebker, and C. Werner, 1988, Satellite radar interferometry: Two-dimensional phase unwrapping, Radio Science, vol. 23, no. 4, pp. 713-720.
12. IEEE Proceedings, Sept 1996, Special Issue on Instantaneous Frequency Estimation, vol. 84, no. 9.
13. IEEE Trans. Signal Process., 2002, Special issue on Monte Carlo methods for statistical signal processing, vol. 50, no. 2.
14. P. Kloeden and E. Platen, 1992, Numerical Solution of Stochastic Differential Equations, Springer-Verlag, New York.
15. T. Li, 1998, Multipath time delay estimation using regression stepwise procedure, IEEE Trans. Signal Process., vol. 46, no. 1, pp. 191-195.
16. R. Lipster and A. Shiryayev, 1978, Statistics of Random Processes, vol. I and II, Springer-Verlag, New York.
17. A. Lipton, 2001, Mathematical Methods for Foreign Exchange, World Scientific Publishing Company, London.
18. S. Neftci, 2000, An Introduction to the Mathematics of Financial Derivatives, Academic Press, New York.
19. B. Oksendal, 1998, Stochastic Differential Equations, Springer-Verlag New York.
20. D. Politis, 1998, Computer-intensive methods in statistical analysis, IEEE Signal Process. Magazine, vol. 15, no. 1, pp. 39-55.
21. B. Prakasa Rao, 1999, Semi Martingales and Their Statistical Inference, Chapman & Hall/CRC, Washington D.C.
22. G. Proakis, 1989, Digital Communication, John Wiley, New York.
23. S. Song, S. Napel, N. Pelc, and G. Glover, 1995, Phase unwrapping of MR phase images using poisson equation, IEEE Trans. Image Process., vol. 4, no. 5, pp. 667-676.
24. R. Souza and A. Neto, 1996, A bootstrap simulation study in ARMA(p, q) structure, J. Forecasting, vol. 15, p. 343-353.
25. H. Van Trees, 1970, Detection, Estimation and Modulation Theory, Part III, John Wiley, New York.
26. D. Welmer, 1995, High Resolution Radar, Artech House, Boston, MA.
27. A. Zaman, 1996, Statistical Foundations for Econometric Techniques Academic Press, New York.
28. A. Zoubir and B. Boashash, 1998, The bootstrap and its application in signal processing, IEEE Signal Process. Magazine, vol. 15, no. 1, pp. 56-76.