Sparse Time-Frequency-Frequency-Rate Representation for Multicomponent Nonstationary Signal Analysis

Though high resolution time-frequency representations (TFRs) are developed and provide satisfactory results for multicomponent nonstationary signals, extracting multiple ridges from the time-frequency (TF) plot to approximate the instantaneous frequencies (IFs) for intersected components is quite difficult. In this work, the sparse time-frequency-frequency-rate representation (STFFRR) is proposed by using the short-time sparse representation (STSR) with the chirp dictionary. The instantaneous frequency rate (IFRs) and IFs of signal components can be jointly estimated via the STFFRR. As there are permutations between the IF and IFR estimates of signal components at different instants, the local k-means clustering algorithm is applied for component linking. By employing the STFFRR, the intersected components in TF plot can be well separated and robust IF estimation can be obtained. Numerical results validate the effectiveness of the proposed method.