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f-wx ferent scales and positions 4 . Different algorithms were proposed to achieve this purpose. In the mid-wx 1970s, Coifman and Wickerhauser 5 developed the automatic decomposition method which had a very strong influence on the development of wavelet the-wx ory. In 1984, Grossman and Morlet 6 proposed the continuous WT which allows the decomposition of a signal into contributions from both he space and scale domains based on the invariance under the affine group, namely, translation and dilation. In wx 1989, Mallat 7 introduced the multi-resolution signal decomposition MRSD algorithm. Daubechies adopted this approach to construct families of com-pact supported wavelets and coupled it to quadrature mirror filtering. This provides a general way for con-structing orthogonal wavelet bases and leads to the . implementation of the fast wavelet transform FWT algorithm.

References

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[2] I. Daubechies Ed. , Ten Lectures on Wavelets, SIAM Press, Philadelphia, 1992.
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[6] A. Grossman, J. Morlet, SIAM J. Math. 15 1984 723–736.
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[12] C.K. Chui Ed. , An Introduction to Wavelets, Academic Press, New York, 1992, p. 49.
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[14] C.K. Chui, L. Montefusco, L. Puccio Eds. , Wavelets: The-ory, Algorithms and Applications, Academic Press, San Diego, 1994.
[15] J.S. Byrnes, J.L. Byrnes, K.A. Hargreaves, K. Berry Eds. , Wavelet and Their Application, Kluwer Academic Publish-ers, The Netherlands, 1994.
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