Reconstruction of Non-Stationary Signals by Inverse Wavelet Transform.

Abstract

Non-stationary signals must be represented in a time-frequency plane because frequencies of those signals evolve with time. For the time-frequency analysis, representative methods, such as spectrogram, Wigner distribution and wavelet transform (WT), have been investigated. WT, in particular, has attracted much attention, because it can detect discontinuous points in signals, and the frequency resolution of WT is similar to that of a human ear. In the case of wavelet analysis, if the admissibility condition is satisfied for the analyzing wavelet applied, the time-frequency distribution can be inversely transformed to the original time series. In this study, comparisons are made between original signals and the inversely transformed time series of the time-frequency distribution obtained by WT for several kinds of signals. It is clarified that the signal reconstruction by means of inverse wavelet transform (IWT) is a very potent method in the field of signal analysis.