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On the diagonal approximation of the auto-correlation function with the wavelet basis which is optimal with respect to the relative entropy

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1 Author(s)
Sakaguchi, F. ; Dept. of Electr. & Electron. Eng., Fukui Univ., Japan

If the covariance function of a random signal can be written in a diagonal form via the wavelet basis, this random signal can be regarded as a superposition of the wavelets which arise randomly. However, it is known that, in general, such an expression is not possible. In this paper, in place of a perfect diagonalization, an optimal approximate diagonalization in the sense of the relative entropy is investigated theoretically. Especially, it is shown that when a set of wavelets forming complete orthonormal sets expressed in a vector form as {φ i} is used as the basis, an optimal diagonal approximation of the covariance matrix Γ is not the diagonal form Σh (φ¯hτΓφh hφ¯hτ using the so-called `wavelet spectrum' but Σh(φ¯hτΓ -1φh)-1φhφ¯ hτ. Further, several examples are given where Haar wavelets are used

Published in:

Circuits and Systems, 1994. APCCAS '94., 1994 IEEE Asia-Pacific Conference on

Date of Conference:

5-8 Dec 1994