Eigenvalues-based time-frequency analysis

Abstract

In this paper, a relationship between parameters of a sinusoidal signal and the significant eigenvalues of Hankel matrix of the sinusoidal signal is derived. Additionally, the mean of magnitude of significant eigenvalue pair (MMSEP) of a sinusoidal signal is compared with the amplitude and length of the sinusoidal signal. Furthermore, a new technique based on the eigenvalue decomposition of Hankel matrix (EVDHM) is proposed to compute the time-frequency distribution (TFD) of a signal. In the proposed technique, the signal is segmented into short-duration frames with the help of a rectangular window. Each frame is decomposed using the EVDHM technique. Then, the mean frequency and 3 dB bandwidth of the decomposed components are computed for each frame. An energy parameter based on MMSEP of the decomposed components is defined for the mean frequency in the time-frequency plane to obtain the TFD of the signal. The energy parameter of the decomposed components represents the signal energy in the time-frequency plane. The effect of the change in window size on the resolution of a signal’s TFD obtained using the proposed method is studied with the help of a synthetic signal. Furthermore, the comparison of TFDs obtained from the proposed method and methods from the literature is performed with the help of a synthetic signal and two real-life signals. The proposed method is found to be providing accurate and high resolution TFD as compared to compared methods. Additionally, the Rényi entropy of the TFDs is compared, and the TFD obtained using the proposed method is found to have the lowest Rényi entropy among the compared methods, indicating superior time-frequency resolution.