Compressive sensing with an overcomplete dictionary for high-resolution DFT analysis

The problem of resolving frequency components close to the Rayleigh threshold, while using time-domain sample sequences of length not greater than N, is relevant to several waveform monitoring applications where acquisition time is upper-bounded. The paper presents a compressive sensing (CS) algorithm that enhances frequency resolution by introducing a dictionary that explicitly accounts for spectral leakage on a fine frequency grid. The proposed algorithm achieves good estimation accuracy without significantly extending total measurement time.