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   -> Volume 3, Issue 11

Preprint: Wavelet Thresholding Techniques for Power Spectrum...
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Author Message (Pierre Moulin)

PostPosted: Mon Dec 02, 2002 1:12 pm    
Subject: Preprint: Wavelet Thresholding Techniques for Power Spectrum...
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Preprint: Wavelet Thresholding Techniques for Power Spectrum...

The following preprint is available by anonymous ftp from
as pub/moulin/wavSE.tar.Z. On UNIX systems:
uncompress wavSE.tar.Z
tar xvf wavSE.tar

Wavelet Thresholding Techniques for Power Spectrum Estimation
(to appear in IEEE Trans. on Signal Processing, Nov. 94)

by P. Moulin

Estimation of the power spectrum $S(f)$ of a stationary random process
can be viewed as a nonparametric statistical estimation problem.
We introduce a nonparametric approach based on a wavelet representation
for the logarithm of the unknown $S(f)$. This approach offers the ability
to capture statistically significant components of $ln S(f)$ at different
resolution levels and guarantees nonnegativity of the spectrum estimator.
The spectrum estimation problem is set up as a problem of inference on
the wavelet coefficients of a signal corrupted by additive non-Gaussian noise.
We propose a wavelet thresholding technique to solve this problem under
specified noise/resolution tradeoffs and show that the wavelet coefficients
of the additive noise may be treated as independent random variables.
The thresholds are computed using a saddle-point approximation to
the distribution of the noise coefficients.
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