Eigenvalue Decomposition of Hankel Matrix-Based Time-Frequency Representation for Complex Signals

Abstract

The analysis of non-stationary signals using time-frequency representation (TFR) presents simultaneous information in time and frequency domain. Most of TFR methods are developed for real-valued signals. In several fields of science and technology, the study of unique information presented in the complex form of signals is required. Therefore, an eigenvalue decomposition of Hankel matrix-based TFR method, which is a data-driven technique, has been extended for the analysis of complex-valued signals. In this method, the positive and negative frequency components of complex signals are separately decomposed using recently developed eigenvalue decomposition of Hankel matrix-based method. Further, the Hilbert transform is applied on decomposed components to obtain TFR for both positive and negative frequency ranges. The proposed method for obtaining TFR is compared with the existing methods. Results for synthetic and natural complex signals provide support to the proposed method to perform better than compared methods.