Time-invariant orthonormal wavelet representations
Time-invariant orthonormal wavelet representations
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DOI：
10.1109/78.533717
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发表时间：
1996-08-01
影响因子：
5.4
通讯作者：
Carfantan, H
中科院分区：
文献类型：
--
作者：
Pesquet, JC;Krim, H;Carfantan, H
从一个所谓的母小波开始，一个简单的正交基的构造，以及一个有效的实现，得到了小波分解容易接受，并产生了很大的研究兴趣，在其应用。然而，标准正交基可能并不总是信号的合适表示，特别是当时间（或空间）不变性是一个必要的属性，解决这个问题的传统方法是使用冗余分解.本文讨论了正交小波变换的时间不变性问题，并提出了小波包分解的一个扩展，我们证明了它可以实现时间不变性和保持正交性，我们随后提出了一种有效的方法来获得这样的分解。我们证明了我们的方法的重要性，考虑在信号重构和时间延迟估计的一些应用实例。
A simple construction of an orthonormal basis starting with a so-called mother wavelet, together with an efficient implementation gained the wavelet decomposition easy acceptance and generated a great research interest in its applications. An orthonormal basis may not, however, always be a suitable representation of a signal, particularly when time (or space) invariance is a required property, The conventional way around this problem is to use a redundant decomposition.In this paper, we address the time-invariance problem for orthonormal wavelet transforms and propose an extension to wavelet packet decompositions, We show that it is possible to achieve time invariance and preserve the orthonormality, We subsequently propose an efficient approach to obtain such a decomposition. We demonstrate the importance of our method by considering some application examples in signal reconstruction and time delay estimation.