26,891 research outputs found
Central Limit Theorems for Wavelet Packet Decompositions of Stationary Random Processes
This paper provides central limit theorems for the wavelet packet
decomposition of stationary band-limited random processes. The asymptotic
analysis is performed for the sequences of the wavelet packet coefficients
returned at the nodes of any given path of the -band wavelet packet
decomposition tree. It is shown that if the input process is centred and
strictly stationary, these sequences converge in distribution to white Gaussian
processes when the resolution level increases, provided that the decomposition
filters satisfy a suitable property of regularity. For any given path, the
variance of the limit white Gaussian process directly relates to the value of
the input process power spectral density at a specific frequency.Comment: Submitted to the IEEE Transactions on Signal Processing, October 200
Covariant representations for matrix-valued transfer operators
Motivated by the multivariate wavelet theory, and by the spectral theory of
transfer operators, we construct an abstract affine structure and a
multiresolution associated to a matrix-valued weight. We describe the
one-to-one correspondence between the commutant of this structure and the fixed
points of the transfer operator. We show how the covariant representation can
be realized on if the weight satisfies some low-pass condition.Comment: new version, motivation adde
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