Prefiltering in Wavelet Analysis Applying Cubic B-Splines

• Autorzy: Rakowski W.

Identyfikatory

DOI

10.2478/eletel-2014-0044

• Języki publikacji: EN

Abstrakty

EN

Wavelet transform algorithms (Mallat’s algorithm, a trous algorithm) require input data in the form of a sequence of numbers equal to the signal projection coefficients on a space spanned by integer-translated copies of a scaling function. After sampling of the continuous-time signal, it is most frequently possible to compute only approximated values of the signal projection coefficients by choosing a specific signal approximation. Calculation of the signal projection coefficients based on the signal interpolation by means of cubic B-splines is proposed in the paper.

Słowa kluczowe

EN

wavelet; scaling function; wavelet analysis; wavelet transform; cubic box spline; digital filters; direct cubic B-spline filter; prefiltering

• Wydawca: Polish Academy of Sciences, Committee of Electronics and Telecommunication
• Czasopismo: International Journal of Electronics and Telecommunications
• Rocznik: 2014
• Tom: Vol. 60, No. 4
• Strony: 331--340
• Opis fizyczny: Bibliogr. 12 poz., wykr.

Twórcy

autor

Rakowski W.

• Faculty of Management of Bialystok University of Technology, Poland

Bibliografia

• [1] S. Mallat, A Wavelet Tour of Signal Processing: The Sparce Way, Third Edition. Academic Press, 2009.
• [2] M. Holschneider, R. Kronland-Martinet, J. Morlet, and P. Tchamitchian, “A real-time algorithm for signal analysis with help of the wavelet transform,” in Wavelets, Time-Frequency Methods and Phase Space, Springer-Verlag, 1989.
• [3] M. J. Shensa, “The discrete wavelet transform: Wedding the a trous and mallat algorithms,” IEEE Transactions on Signal Processing, vol. 40, no. 10, pp. 2464-2482, 1992.
• [4] M. Unser, “Splines: A perfect fit for signal and image processing,” IEEE Signal Processing Magazine, pp. 22-38, 1999.
• [5] A. V. Oppenheim, A. S. Willsky, and S. H. Nawab, Signals and Systems. Prentice-Hall International, Inc., 2/E, 1997.
• [6] J. G. Proakis and D. G. Manolakis, Digital Signal Processing. Pearson Prentice Hall, 2007.
• [7] M. Unser, A. Aldroubi, and M. Eden, “B-spline signal processing: Part I - theory,” IEEE Transactions on Signal Processing, Vol. 41, No. 2, pp. 821-833, 1993.
• [8] M. Unser, A. Aldroubi, and M. Eden, “B-spline signal processing: Part II - efficient design and applications,” IEEE Transactions on Signal Processing, Vol. 41, No. 2, pp. 834-848, 1993.
• [9] G. Strang and T. Nguyen, Wavelets and Filter Banks. Wellesley-Cambridge Press, 1996.
• [10] B. R. Johnson and J. L. Kinsey, “Quadrature prefilters for discrete wavelet transform,” IEEE Transactions on Signal Processing, Vol. 48, No.3, pp. 873-875, 2000.
• [11] J. Zhank and Z. Bao, “Initialization of orthogonal discrete wavelet transforms,” IEEE Transactions on Signal Processing, Vol. 48, No. 5, pp. 1474-1477, 2000.
• [12] S. Ericsson and N. Grip, “Efficient wavelet prefilters with optimal timeshifts,” IEEE Transactions on Signal Processing, Vol. 53, No. 7, 2451-2461, 2005.