Fractional generalized splines and signal processing

Signal Processing

Volumn 86, Issue 9, 2006, Pages 2340-2350

  Panda, Rutuparna ^a   Dash, Madhumita ^a  

^a VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY   (India)

Author keywords

Approximation; Fractional generalized splines; Fractional wavelet transform; Interpolation; Symmetrical functions

Indexed keywords

COMPUTER SIMULATION; DIFFERENTIAL EQUATIONS; FINITE DIFFERENCE METHOD; FREQUENCY DOMAIN ANALYSIS; OPTIMIZATION; SIGNAL PROCESSING;

FRACTIONAL GENERALIZED SPLINES; FRACTIONAL WAVELET TRANSFORMS; SYMMETRICAL FUNCTIONS;

SPLINES;

EID: 33745739434     PISSN: 01651684     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.sigpro.2005.10.017     Document Type: Article

References (29)

1. Alberg J.H., Nilson E.N., and Walsh J.L. The Theory of Splines and Their Applications (1967), Academic Press, New York
2. de Boor C. A Practical Guide to Splines (1978), Springer, New York
3. Schoenberg I.J. Contribution to the problem of approximation of equidistant data by analytic functions. Quart. Appl. Math. 4 (1946) 45-99 and 112-141
4. Schumaker L.L. Spline Functions: Basic Theory (1981), Wiley, New York
5. Panda R., Rath G.S., and Chatterji B.N. Generalized B-spline signal processing. Signal Processing 55 (November 1996) 1-14
6. Panda R., and Chatterji B.N. Least squares generalized B-spline signal and image processing. Signal Processing 81 10 (October 2001) 2005-2017
7. Unser M., and Blu T. Fractional splines and wavelets. SIAM Rev. 42 1 (January 2000) 43-67
8. Blu T., and Unser M. Wavelets, fractals and radial basis functions. IEEE Trans. Signal Processing 50 3 (March 2002) 543-553
9. Panda R., and Chatterji B.N. B-spline signal processing using harmonic basis functions. Signal Processing 72 (February 1999) 147-166
10. Unser M., Aldroubi A., and Eden M. A family of polynomial spline wavelet transforms. Signal Processing 30 (1993) 141-162
11. Unser M., Aldroubi A., and Eden M. B-spline signal processing: Part II-efficient design and implementations. IEEE Trans. Signal Processing 41 (1993) 834-848
12. Kreyszig E. Advanced Engineering Mathematics (1994), Wiley Eastern Ltd.
13. Nishimoto K. Fractional Calculus (1989), Descartes Press Co., Koriyama, Japan
14. Ortigueira M.D. Introduction to fractional signal processing. Part I: Continuous-time systems. IEE Proc. Vis. Image Signal Processing 1 (February 2000) 62-70
15. M.D. Ortigueira, Symmetric fractional spline, Special issue of Signal Processing (November 2003).
16. Chui C.K. An Introduction to Wavelets (1992), Academic Press, Boston, MA
17. Herley C., and Vetterli M. Wavelets and recursive filter banks. IEEE Trans. Signal Processing 41 (August 1993) 2536-2556
18. P.G. Lemarii, Y. Meyer, Ondelletes et bases Hibertienness Radista, Mathematica Ibero Americanes, vol. 2, 1986.
19. Mallat S.G. A theory for multiresolution signal decomposition: the wavelet representation. IEEE Trans. Pattern Anal. Mach. Intell. 11 (July 1989) 674-693
20. Mallat S.G. Multifrequency channel decomposition of images and wavelet models. IEEE Trans. Accoust. Speech Signal Processing 37 (December 1989) 2091-2110
21. 2(R). Trans Am. Math. Soc. 315 (1989) 69-87
22. Meyer Y. Wavelets: Algorithms and Applications (1993), SIAM, Philadelphia, PA
23. Vetterli M., and Herley C. Wavelets and filters banks: theory and design. IEEE Trans. Signal Processing 40 (September 1992) 2207-2232
24. Vetterli M., and Kovacevic J. Wavelets and Sub-band Coding (1995), Prentice-Hall, Englewood Cliffs, NJ
25. Battlě G. A block spin construction of ondelettes, Part-I: Lemarie functions. Comm. Math. Phys. 110 (1987) 601-615
26. Aldroubi A., and Unser M. Sapmling procedures in function spaces and asymptotic convergence with Shannon's sampling theory. Numer. Funct. Anal. Optim. 15 (1994) 1-21
27. Oppenheim A.V., and Schafer R.W. Digital Signal Processing (1988), Prentice-Hall of India Pvt. Ltd., New Delhi
28. Proakis J.G., and Manolakis D.G. Digital Signal Processing: Principles, Algorithms and Applications (2000), Prentice-Hall of India Pvt. Ltd., New Delhi
29. Strang G., and Nguyen T. Wavelets and Filter Banks (1996), Wellsky-Cambridge, Wellsky, MA