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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。
Classical wavelet packet transform will reduce the length of the decomposition sequence, which in some areas is not very favorable. In order to solve this problem, this paper proposes a convolutional wavelet packet transform algorithm. By using this transform, the length of each channel sequence obtained after decomposition is consistent with the original signal no matter how many layers the signal is decomposed by wavelet packet. In this paper, the fast algorithm of the positive and inverse transform of convolutional wavelet packet is deduced. Taking the processing of an actual signal as an example, the results are compared with the classical wavelet packet analysis. Their results are consistent, but the convolution Type wavelet packet is removed from the process of restructuring this process.