Some Results on the Wavelet Packet Decomposition of Nonstationary Processes

Some Results on the Wavelet Packet Decomposition of Nonstationary Processes

Wavelet/wavelet packet decomposition has become a very useful tool in describing nonstationary processes. Important examples of nonstationary processes encountered in practice are cyclostationary processes or almost-cyclostationary processes. In this paper, we study the statistical properties of the wavelet packet decomposition of a large class of nonstationary processes, including in particula...

Wavelet packet modelling of nonstationary time seriesGuy

Wavelet packet modelling of nonstationary time series

This article models the relationship between a response time series, fYtgt2Zand an explanatory time series fXtgt2Z. We hope that any model we choose might be interesting in its own right but we shall also be interested in using it to predict future values of Yt from future values of Xt. When both time series fall into the class of ARMA type models then it is appropriate to use \transfer functio...

Wavelet packet transfer function modelling of nonstationary time series

This article shows how a non-decimated wavelet packet transform (NWPT) can be used to model a response time series, Yt, in terms of an explanatory time series, Xt. The proposed computational technique transforms the explanatory time series into a NWPT representation and then uses standard statistical modelling methods to identify which wavelet packets are useful for modelling the response time ...

Spectrum Flipping for Wavelet Packet Decomposition

In this paper, it is shown that the higher compression performance of biorthogonal wavelet filters over orthogonal wavelet filters is the combined effect from (1) the asymmetry of the frequency responses of the biorthogonal wavelet filters and (2) the non-flat spectra of the signals to be decomposed. Based upon this observation, an improved wavelet packet decomposition method for natural images...