Wavelet Transform With Tunable Q-Factor
Wavelet Transform With Tunable Q-Factor
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DOI：
10.1109/tsp.2011.2143711
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发表时间：
2011-08-01
影响因子：
5.4
通讯作者：
Selesnick, Ivan W.
中科院分区：
文献类型：
--
作者：
Selesnick, Ivan W.
本文描述了一种离散时间小波变换，其Q因子是很容易指定的。因此，可以根据其所应用的信号的振荡行为来调谐变换。该变换是基于一个实值的缩放因子（膨胀因子），并实现了使用一个完美的重建过采样滤波器组与实值采样因子。提出了两种形式的变换。第一种形式定义为离散时间信号定义在所有。第二种形式定义为有限长度的离散时间信号，可以有效地实现与FFT。该变换通过其Q因子和其过采样率（冗余）来参数化，具有适度的过采样率（例如，三到四倍过完全）足以使分析/合成功能很好地局部化。
This paper describes a discrete-time wavelet transform for which the Q-factor is easily specified. Hence, the transform can be tuned according to the oscillatory behavior of the signal to which it is applied. The transform is based on a real-valued scaling factor (dilation-factor) and is implemented using a perfect reconstruction over-sampled filter bank with real-valued sampling factors. Two forms of the transform are presented. The first form is defined for discrete-time signals defined on all of. The second form is defined for discrete-time signals of finite-length and can be implemented efficiently with FFTs. The transform is parameterized by its Q-factor and its oversampling rate (redundancy), with modest oversampling rates (e.g., three to four times overcomplete) being sufficient for the analysis/synthesis functions to be well localized.