Construction of a class of compactly supported symmetric and balanced refinable function vector by GTST

Applied Mathematics and Computation

Volumn 207, Issue 1, 2009, Pages 83-89

  Yang, Shouzhi ^a   Huang, Yongdong ^b  

^a SHANTOU UNIVERSITY   (China)

^b Northwest Secondly National College   (China)

Author keywords

Balanced order; GTST; Refinable function vector; Symmetry

Indexed keywords

FUNCTIONS; PROBABILITY DENSITY FUNCTION;

BALANCED ORDER; GTST; REFINABLE FUNCTION VECTOR; SCALE SIMILARITIES; SYMMETRY;

VECTORS;

EID: 58249094727     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2007.10.066     Document Type: Article

References (23)

1. Lebrun J., and Vetterli M. Balanced multiwavelets theory and design. IEEE Trans. Signal Process. 46 4 (1998) 1119-1125
2. J. Lebrun, M. Vetterli, High order balanced multiwavelets, in: Proceedings of the IEEE International Conference Acoustics, Speech and Signal Processing, vol. 3, 1998, pp. 1529-1532.
3. Lebrun J., and Vetterli M. High-order balanced multiwavelets: theory, factorization, and design. IEEE Trans. Signal Process. 9 49 (2001) 1918-1930
4. Lixin S., and Huat T.H. On a family of orthonormal scalar wavelets and related balanced multiwavelets. IEEE Trans. Signal Process. 7 49 (2001) 1447-1453
5. Selesnick I.W. Balanced GHM-like multiscaling functions. IEEE Trans. Signal Process. Lett. 6 (1999) 111-112
6. Lian J.A., and Chui C.K. Balanced multiwavelets with short filters. IEEE Trans. Signal Process. 11 2 (2004) 75-78
7. s. Math. Comput. 74 (2005) 1323-1344
8. Yang S.Z., and Peng L.Z. Construction of high order balanced multiscaling functions via PTST. Sci. China, Ser. F 49 (2006) 504-515
9. Bacchelli S., Cotronei M., and Lazzaro D. An algebraic construction of k-balanced multiwavelets via the lifting scheme. Numer. Algor. 23 (2000) 329-356
10. Xie C.Z., and Yang S.Z. Construction of refinable function vector via GTST. Appl. Math. Comput. 194 2 (2007) 425-430
11. Plonka G. Approximation order provided by refinable function vectors. Constr. Approx. 13 (1997) 221-244
12. Plonka G., and Strela V. Construction of multiscaling functions with approximation and symmetry. SIAM J. Math. Anal. Appl. 29 (1998) 481-510
13. V. Strela, Multiwavelets theorem and applications, Ph.D. thesis, MIT, 1996.
14. Yang S.Z., and Peng L.Z. Raising approximation order of refinable vector by increasing multiplicity. Sci. China Ser. A 49 (2006) 86-97
15. Vaidyanathan P.P. Multirate Systems and Filter Banks (1993), Simon and Schuster
16. Daubechies I., and Lagarias J.C. Two-scale difference equations. I. Existence and global regularity of solutions. SIAM J. Math. Anal. 22 (1991) 1388-1410
17. Daubechies I., and Lagarias J.C. Two-scale difference equations. II. Local regularity, infinite products of matrices and fractals. SIAM J. Math. Anal. 23 (1992) 1031-1079
18. Jiang Q.T., and Shen Z.W. On existence and weak stability of matrix refinable functions. Constr. Approx. 15 (1999) 337-353
19. Shen Z.W. Refinable function vectors. SIAM J. Math. Anal. 29 (1998) 235-250
20. Chui C.K., and Lian J.A. A study on orthonormal multiwavelets. J. Appl. Numer. Math. 20 (1996) 273-298
21. Lian J.A. Orthogonal criteria for multiscaling functions. Appl. Comput. Harmon. Anal. 5 (1998) 277-311
22. Goodman T.N.T., and Micchelli C.A. On refinement equations determined by Pólya frequency sequences. SIAM J. Math. Anal. 23 (1992) 766-784
23. Geronimo J., Hardin D.P., and Massopust P. Fractal functions and wavelet expansions based on several scaling functions. J. Approx. Theory 78 (1998) 373-401