To solve the problem that the random distribution of noise in the time-frequency (TF) plane largely affects the readability of TF representations, a novel signal adaptive decomposition algorithm processed in TF domain, which provides adequate information about the time-varying instantaneous frequency, is presented in this paper. The theoretical basis of this algorithm is short-time Fourier transform (STFT). The research into the algorithm comprises two steps: the TF plane denoising takes sparse low-rank matrix estimation as a priority and then achieves signal decomposition based on reassignment vector (RV). A low-rank matrix approximation scheme, which exploits the sparse properties of the TF transformation coefficient and uses non-convex penalty, is put forward to obtain clean STFT. Then, a new approach called RV, which is different from the traditional mode decomposition methods such as Empirical Mode Decomposition (EMD), is used to estimate the characteristic curve corresponding to the TF ridges of the interested modes. Based on the classical reassignment method, RV has a solid theory foundation. Moreover, it can identify different signal components such as stationary signal, modulating signal and impulse characteristic. Combining the advantages of low-rank matrix approximation approach and those of RV defined in TF plane, a novel signal adaptive decomposition method is proposed in this paper to identify fault characteristics. To illustrate the effectiveness of the method, fault signals of rolling bearing under stationary condition and time-varying speed are respectively analyzed.
Millimeter Wave Time-Varying Channel Estimation via Exploiting Block-Sparse and Low-Rank Structures