Central Limit Theorems for Wavelet Packet Decompositions of Stationary Random Processes

被引:13
作者
Atto, Abdourrahmane M. [1 ]
Pastor, Dominique [1 ]
机构
[1] Uni Europeenne Bretagne, Inst TELECOM TELECOM Bretagne, F-29238 Brest 3, France
关键词
Band-limited stochastic processes; spectral analysis; wavelet transforms; FILTERS;
D O I
10.1109/TSP.2009.2031726
中图分类号
TM [电工技术]; TN [电子技术、通信技术];
学科分类号
0808 ; 0809 ;
摘要
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 M-band wavelet packet decomposition tree. It is shown that if the input process is 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.
引用
收藏
页码:896 / 901
页数:6
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