Adaptive Fourier series-a variation of greedy algorithm

Advances in Computational Mathematics

Volumn 34, Issue 3, 2011, Pages 279-293

  Qian, Tao ^a   Wang, Yan Bo ^a  

^a UNIVERSITY OF MACAU   (Macao)

Author keywords

Adaptive decomposition of functions; Analytic signal; Blaschke product; Complex hardy space; Greedy algorithm; Instantaneous frequency; Mono components; Rational orthonormal system

Indexed keywords

EID: 79952450818     PISSN: 10197168     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10444-010-9153-4     Document Type: Article

References (21)

1. Akcay, H., Niness, B.: Orthonormal basis functions for modelling continuous-time systems. Signal Process. 77, 261-274 (1999).
2. Bultheel, A., Carrette, P.: Takenaka-Malmquist basis and general Toeplitz matrices. SIAM J. Opt. 41, 1413-1439 (2003).
3. Bultheel, A., Gonzalez-Vera, P., Hendriksen, E., Njastad, O.: Orthogonal rational functions. In: Cambridge Monographs on Applied and Computational Mathematics, vol. 5. Cambridge University Press (1999).
4. Davis, G., Mallat, S., Avellaneda, M.: Adaptive greedy approximations. Constr. Approx. 13, 57-98 (1997).
5. Garnett, J. B.: Bounded Analytic Functions. Academic, New York (1987).
6. Zhu, K.: Spaces of Holomorphic Functions in the Unit Ball. GTM, Springer, New York (2005)3.
7. Hedenmalm, H., Korenblum, B., Zhu, K.: Theory of Bergman Spaces. GTM, Springer, New York (2000).
8. Mallat, S., Zhang, Z.: Matching pursuits with time-frequency dictionaries. IEEE Trans. Signal Process. 41, 3397-3415 (1993).
9. Ninness, B., Hjalmarsson, H., Gustafsson, F.: Generalized Fourier and Toeplitz results for rational orthonormal bases. SIAM J. Control Optim. 37(2), 429-460 (1999).
10. Partington, J. R.: Interpolation, Identification and Sampling, pp. 44-47. Clarendon Press, Oxford (1997).
11. Heuberger, P. S. C., van den Hof, P. M. J., Wahlberg, B.: Modelling and Identification with Rational Orthogonal Basis Functions. Springer, London (2005).
12. Qian, T.: Mono-components for decomposition of signals. Math. Methods Appl. Sci. 29, 1187-1198 (2006).
13. Qian, T.: Boundary derivative of the phases of inner and outer functions and applications. Math. Methods Appl. Sci. 32, 253-263 (2009).
14. Qian, T., Ho, I. T., Leong, I. T., Wang, Y. B.: Adaptive decomposition of functions into pieces of non-negative instantaneous frequencies. Accepted by International Journal of Wavelets, Multiresolution and Information Processing, vol. 8(5) (2010).
15. Qian, T., Wang, R., Xu, Y. S., Zhang, H. Z.: Orthonormal bases with nonlinear phases. Adv. Comput. Math. 33, 75-95 (2010).
16. Qian, T., Xu, Y. S., Yan, D. Y., Yan, L. X., Yu, B.: Fourier spectrum charaterization of hardy spaces and applications. Proc. Am. Math. Soc. 137, 971-980 (2009).
17. Temlyakov, V. N.: Greedy algorithm and m-term trigonometric approximation. Constr. Approx. 107, 569-587 (1998).
18. Tan, L. H., Shen, L. X., Yang, L. H.: Rational orthogonal bases satisfying the Bedrosian identity. Adv. Comput. Math. doi: 10. 1007/s10444-009-9133-8.
19. Walsh, J. L.: Interpolation and Approximation by Rational Functions in the Complex Plane. AMS (1969).
20. Wang, R., Xu, Y. S., Zhang, H. Z.: Fast non-linear Fourier expansions. AADA 1(3), 373-405 (2009).
21. Xu, Y. S., Yan, D. Y.: The Bedrosian identity fot the Hilbert transform of product functions. Proc. Am. Math. Soc. 134, 2719-2728 (2006).