This paper describes a nonstationary spectral analysis method and its application to prognosis and diagnosis of automobiles. An instantaneous frequency spectrum is considered first at a single point of time based on the instantaneous representation of autocorrelation. The spectral distortion is then considered on two-dimensional spectrum, and the filtering is introduced into the instantaneous autocorrelations. By the above procedure, the Instantaneous Covariance method (ICOV), the Instantaneous Maximum Entropy Method (IMEM), and the Wigner method are shown and they are unified. The IMEM is used for the time-dependent spectral estimation of vibration and acoustic sound signals of automobiles. A multi-dimensional (M-D) space is composed based on the variables which are obtained by the IMEM. The M-D space is transformed into a simple two-dimensional (2-D) plane by a projection matrix chosen by the experiments. The proposed method is confirmed useful to analyze nonstationary signals, and it is expected to implement automatic supervising, prognosis and diagnosis for a traffic system.

Analysis of electroencephalogram (EEG) is presented for sleep physiology. This analysis is performed by the Instantaneous Maximum Entropy Method (IMEM), which was given by the author. Appearance and continuation of featuristic waves are not steady in EEG. The characteristics of these waves responding to epoch of sleep are analyzed. The behaviours of waves were clarified by this analysis as follows; (a) time dependent frequency of continuous oscillations of alpha rhythm was observed precisely. Sleep spindles were detected clearly within NREM and these parameters of time, frequency, and peak energy were specified. (b) delta waves with very low frequencies and sleep spindles were observed simultaneously. And (c) the relationship of sleep spindles and delta waves was first detected with negative correlation along time-axis. The analysis by the IMEM was found effective comparing conventional analysis method of FFT, bandpass filter bank, etc.

An analysis method is proposed for nonstationary waveforms. Modelling of a nonstationary waveform is first given in this paper. A waveform is represented by multiple oscillations. The instantaneous phase angle of each oscillation is written by three terms, predictive component, residual component, and initial phase constant. By this modelling, waveform analysis results in estimations of frequency, calculation of residual pbase in instantaneous phase angle. The Instantaneous Maximum Entropy Methods (IMEN) is utilized for frequency estimation. The residual phase angle is obtained by the Vandermonde matrix and the condition of continuity of phase angle among n-neighbourhood. Another analysis method is also proposed by the normalization of waveform parameters. The evaluation of the proposed method is done using artificially composed waveform signals. Novel and useful knowledge was provided by this analysis.