Abstract
It is well known that discrete wavelet transform (DWT) is sensitive to shift, which means a slight shift of feature in the original signal may cause unpredictable changes in the analysis subbands. Some modified versions of DWT can reduce the shift sensitivity, however, they are all redundant. In this article, we shows the shift sensitivity is caused by the aliasing terms formed in the downsampling operation during analysis process. A novel scheme for the design of wavelet is proposed to reduce the effect of aliasing terms as much as possible in the general framework of DWT. A few of biorthogonal wavelets have been designed and applied in the simulation examples. The results of examples demonstrate the efficiency of the designed wavelets in the term of shift insensitivity and nonredundancy.
Highlights
Discrete wavelet transform (DWT) has been applied in many fields as a tool of signal processing, e.g., signal denoising, feature extraction, pattern recognition and image registration [1-3]
We focus on the design of biorthogonal wavelets because they are symmetrical and have been used in many fields
For the general wavelets, the aliasing terms formed in analysis process of DWT can be eliminated in the synthesis process by the anti-aliasing properties of filter banks
Summary
Discrete wavelet transform (DWT) has been applied in many fields as a tool of signal processing, e.g., signal denoising, feature extraction, pattern recognition and image registration [1-3]. Some new wavelets and modified calculation frameworks of DWT have been presented to reduce the shift sensitivity. The shift sensitivity of DWT Consider the calculation framework of DWT using biorthogonal wavelet, in which H0 and H0(z) denote the analysis and synthesis filters in the low-pass branch. The aliasing terms brings out the shift sensitivity in the low-pass analysis output.
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