Prefiltering in Wavelet Analysis Applying Cubic B-Splines

Waldemar Rakowski

Abstract


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.

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REFERENCES

S. Ericsson and N. Grip, “Efficient wavelet prefilters with optimal timeshifts,”

IEEE Transactions on Signal Processing, Vol. 53, No. 7, 2451 -

, 2005.

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.

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.

S. Mallat, A Wavelet Tour of Signal Processing: The Sparce Way, Third

Edition. Academic Press, 2009.

A. V. Oppenheim, A. S. Willsky, and S. H. Nawab, Signals and Systems.

Prentice-Hall International, Inc., 2/E, 1997.

J. G. Proakis and D. G. Manolakis, Digital Signal Processing. Pearson

Prentice Hall, 2007.

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.

G. Strang and T. Nguyen, Wavelets and Filter Banks. Wellesley -

Cambridge Press, 1996.

M. Unser, “Splines: A perfect fit for signal and image processing,” IEEE

Signal Processing Magazine, pp. 22-38, 1999.

M. Unser, A. Aldroubi, and M. Eden, “B-spline signal processing: Part i - theory,” IEEE Transactions on Signal Processing, Vol. 41, No. 2, pp.

-833, 1993.

——, “B-spline signal processing: Part ii - efficient design and applications,”

IEEE Transactions on Signal Processing, Vol. 41, No. 2, pp. 834

- 848, 1993.

J. Zhank and Z. Bao, “Initialization of orthogonal discrete wavelet

transforms,” IEEE Transactions on Signal Processing, Vol. 48, No. 5,

pp. 1474 - 1477, 2000.


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