Abstract
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.