Wavelet Approximation of Deterministic and Random Signals: Convergence Properties and Rates

IEEE Transactions on Information Theory

Volumn 40, Issue 4, 1994, Pages 1013-1029

  Cambanis, Stamatis ^a   Masry, Elias ^b  

^a UNIVERSITY OF NORTH CAROLINA   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

rates of convergence; second order random processes; Wavelet orthonormal expansions

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; CORRELATION THEORY; ERRORS; INFORMATION THEORY; INTEGRAL EQUATIONS; MATHEMATICAL MODELS; MATHEMATICAL TRANSFORMATIONS; RANDOM PROCESSES; SIGNAL PROCESSING;

CORRELATION FUNCTION; FINITE INTERVALS; MULTIRESOLUTION SIGNAL DECOMPOSITION; RATES OF CONVERGENCE; SECOND ORDER RANDOM PROCESSES; STATISTICAL SIGNAL ANALYSIS; WAVELET ORTHONORMAL EXPANSION;

SIGNAL THEORY;

EID: 0028462624     PISSN: 00189448     EISSN: 15579654     Source Type: Journal    
DOI: 10.1109/18.335971     Document Type: Article

References (14)

1. M. Abramowitz and L. A. Stegun, Handbook of Mathematical Functions. Washington, DC: National Bureau of Standards, Appl. Math. Series, vol. AMS 55, 1968.
2. A. Cohen, J. Froment, and J. Istas, “Analyse multiresolution des signaux aléatoires,” C.R. Acad. Sci. Paris, vol. 312, ser. I, pp. 567-570, 1991.
3. I. Daubechies, Ten Lectures on Wavelets. Philadelphia, PA: SIAM, 1992.
4. R. A. Devore, B. Jawerth, and B. J. Lucier, “Image compression through wavelet transform coding,” IEEE Trans. Inform. Theory, vol. 38, pp. 719-746, Mar. 1992.
5. M. J. Genossar, M. Goldburg, H. Lev-Ari, and T. Kailath, “Extending wavelet decompositions to random processes with applications to periodically correlated processes,” Tech. Rep. 91-GGLK-1, Inform. Syst. Lab., Stanford Univ., Stanford, CA, Aug. 1991.
6. R. A. Gopinath and C. S. Burrus, “Wavelet transforms and filter banks,” in Wavelets: A Tutorial in Theory and Applications, C. K. Chui, Ed. Boston, MA: Academic, 1992, pp. 603-654.
7. V. I. Krylov, Approximate Calculation of Integrals. New York: Macmillan, 1962.
8. S. G. Mallat, “A theory of multiresolution decomposition: The wavelet representation,” IEEE Trans. Pattern Anal. Machine Intell., vol. 11, pp. 674-693, July 1989.
9. —, “Multiresolution approximations and wavelet orthonormal bases of L2(R),” Trans. Amer. Math. Soc., vol. 315, pp. 69-87, Sept. 1989.
10. E. Masiy, “Convergence properties of wavelet series expansions of fractional Brownian motion,” submitted for publication, Nov. 1992.
11. Y. Meyer, Ondelettes et Opérateurs I, Ondelettes. Paris, France: Hermann, 1990; Wavelets and Operators. Cambridge, England: Cambridge Univ. Press, 1992.
12. J. F. Steffensen, Interpolation. Baltimore, MD: Williams & Wilkins, 1927.
13. A. H. Tewfik, D. Sinha, and P. Jorgensen, “On the optimal choice of a wavelet for signal representation,” IEEE Trans. Inform. Theory, vol. 38, pp. 747-765, Mar. 1992.
14. P. W. Wong, “Wavelet decomposition of harmonizable random processes,” IEEE Trans. Inform. Theory, vol. 39, pp. 7-18, Jan. 1993.