Time-frequency distributions have been used to provide high resolutionrepresentation in a large number of signal processing applications. However,high resolution and accurate instantaneous frequency (IF) estimation usuallydepend on the employed distribution and complexity of signal phase function. Toensure an efficient IF tracking for various types of signals, the class ofcomplex time distributions has been developed. These distributions facilitateanalysis in the cases when standard distributions cannot provide satisfactoryresults (e.g., for highly nonstationary signal phase). In that sense, anambiguity based form of the forth order complex-time distribution isconsidered, in a new compressive sensing (CS) context. CS is an intensivelygrowing approach in signal processing that allows efficient analysis andreconstruction of randomly undersampled signals. In this paper, the randomlychosen ambiguity domain coefficients serve as CS measurements. By exploitingsparsity in the time-frequency plane, it is possible to obtain highlyconcentrated IF using just small number of random coefficients from ambiguitydomain. Moreover, in noisy signal case, this CS approach can be efficientlycombined with the L-statistics producing robust time-frequency representations.Noisy coefficients are firstly removed using the L-statistics and thenreconstructed by using CS algorithm. The theoretical considerations areillustrated using experimental results.
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