Reconstruction of non stationary signals by inverse transform of Wigner distribution

Non stationary signals must be represented in a time-frequency plane, because the frequency of those signals evolve with time. For the time-frequency analysis, some representative methods such as spectrogram, Wigner distribution (WD) and wavelet transform (WT) have been investigated. When a certain kind of data processing is applied to the time-frequency two-dimensionally analyzed signals and the effects of the processing are examined, those signals must be inversely transformed to the time domain. Time-frequency two-dimensionally analyzed signals derived from WT can be easily reconstructed into the time domain. In this study, the inverse transform algorithm of WD (IWD) is developed. In the inverse transform algorithms of RID and BLMSWD, both of which are proposed to reduce interference terms of WD, the reconstructed results closely agree with original simulated signals. For the analysis of a measured phonetic signal, inverse transform algorithms of RID and BLMSWD are applied and results are compared with those calculated from the inverse wavelet transform (IWT). Close agreement is obtained between the measured signal and that calculated using IWT. It is clarified that reconstructions from the inverse transform of RID and BLMSWD give satisfactory results.