Sparse time–frequency representation for signals with fast varying instantaneous frequency

Abstract

Time–frequency (TF) distributions have been used for providing high-resolution representation in a large number of signal processing applications. However, high resolution and accurate instantaneous frequency (IF) estimation usually depends on the employed distribution and complexity of signal phase function. To ensure an efficient IF tracking for various types of signals, a class of complex-time distributions (CTD) has been developed. These distributions facilitate analysis in cases when standard distributions cannot provide satisfactory results (e.g. for highly non-stationary signal phase). In that sense, an ambiguity-based form of the fourth-order CTD is considered, in a new compressive sensing (CS) context. CS is an intensively growing approach in signal processing that allows efficient analysis and reconstruction of randomly under-sampled signals. In this study, randomly chosen ambiguity domain coefficients serve as CS measurements. By exploiting sparsity in the TF plane, it is possible to obtain highly concentrated IF using just small number of randomly chosen coefficients from the ambiguity domain. Moreover, in noisy signal case, this CS approach can be efficiently combined with the L-statistics producing robust TF representations. Noisy coefficients are first removed using the L-statistics and then reconstructed by using the CS algorithms. The theoretical considerations are illustrated using experimental results.