Convolution wavelet packet transform and its applications to signal processing

The length of decomposition results of traditional wavelet packet transform (WPT) will decrease by half in the next level for downsampling, then the length of sequences in the last level will become very short, and this is very inconvenient for further analysis of these sequences. One kind of WPT based on convolution definition is put forward, its fast decomposition and reconstruction algorithms are given, and the outstanding characteristic of this convolution WPT is that no matter how many levels a signal is decomposed, the length of sequences got in every level will never decrease and can always keep the same as that of the original signal, so the defect of traditional WPT is overcome. For traditional WPT, to achieve the same effect of direct decomposition of convolution WPT, reconstruction operation must be done and the calculation will greatly increase. Based on the length invariance property of convolution WPT, a noise reduction algorithm is proposed, and signal processing example shows that its denoising performance is better than that of traditional WPT, and also much better than that of wavelet transform.