Discrete wavelet transform based shift invariant analysis scheme for transient sound signals

Discrete wavelet transform (DWT) has gained widespread recognition and popularity in signal processing due to its ability to underline and represent time-varying spectral properties of many transient and other nonstationary signals. However, DWT is a shift-variant transform. This shift-variance is a major problem with the use of DWT for transient signal analysis and pattern recognition applications. A number of modified forms of DWT have been investigated in recent years that provide approximate shift-invariant transform but at the cost of increased redundancy and complexity. In this paper, a shift-invariant analysis scheme is proposed which is non-redundant. This scheme combines minimum-phase (MP) reconstruction with the DWT so that the resultant scheme provides a shift-invariant transform. The detailed properties of MP signal and different methods to reconstruct it are explained. The proposed scheme can be used for the analysis-synthesis, classification, and compression of transient sound signals