卷积型小波包变换及其快速算法

The Transformation of Convolution Type of Wavelet Packet and Its' Fast Algorithm

经典的小波包变换会使分解序列的长度递减,这在某些领域并不是很有利。为了解决这一问题,本文提出了卷积型小波包变换算法,利用这种变换,不管信号被小波包分解多少层,分解得到的各频道序列长度始终与原始信号一致。文中推导了卷积型小波包的正变换和逆变换的快速算法,并以对一个实际信号的处理为例,与经典的小波包分析结果进行了比较,它们的效果是一致的,但是卷积型小波包却免去了重构这一过程的手续。

The length of sequences obtained in the classical wavelet packet transformation always decreases by degrees and this is not an expecting result in some field. In order to solve this problem, the transformation of convolution type of wavelet packet is put forward in this paper. The outstanding characteristic of this type of transformation is that no matter how many layers the signal is decomposed by the wavelet packet, the length of every sequence in different channels will always keep the same length as that of original signals. The fast algorithms for the forward and inverse transformation of this type of wavelet packet are induced in this paper. An example of one signal processed by this new transformation is given also. Compared with the classical wavelet packets analyzing result, the convolution type of wavelet packet has the same processing effect, but the procedure of reconstruction is avoided.