平稳随机过程小波包分解的中心极限定理
Central Limit Theorems for Wavelet Packet Decompositions of Stationary Random Processes
摘要：
本文给出了平稳带限随机过程小波包分解的中心极限定理。对在$M$带小波包分解树的任意给定路径的节点处返回的小波包系数序列进行渐近分析。结果表明，如果输入过程是中心和严格平稳的，这些序列收敛分布白高斯过程时，分辨率水平的增加，只要分解滤波器满足一个合适的属性的规律性。对于任何给定路径，极限白高斯过程的方差直接与特定频率处的输入过程功率谱密度的值相关。
英文摘要：
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 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
