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Eigenvalues-based time-frequency analysis
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DOI：10.1016/j.jfranklin.2026.108561.png)
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Abstract
En 中文
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 R & eacute;nyi entropy of the TFDs is compared, and the TFD obtained using the proposed method is found to have the lowest R & eacute;nyi entropy among the compared methods, indicating superior time-frequency resolution.
Keywords:
Eigenvalue decomposition of Hankel matrix
Signal analysis
Short-duration analysis
Time-frequency distribution
Journal
J
IF:
4.2
Papers:
822
Citations:
0