High-accuracy frequency estimation in compressive sensing-plus-DFT spectral analysis

Accurate measurement of a multisine waveform is a classic spectral analysis problem. Algorithms based on the discrete Fourier transform (DFT) need to deal with spectral leakage, which adversely affects both amplitude estimation accuracy and frequency resolution. Approaches where a parametric signal model is identified can achieve much better frequency resolution, at the price of greater complexity. The class of super-resolution algorithms based on compressive sensing (CS) represents a new non-parametric alternative that allows a significant increase in the density of the frequency grid, although continuous-valued frequency estimates still cannot be obtained. A recently proposed algorithm called continuous basis pursuit (CBP) achieves this goal by formulating a more complex constrained convex optimization problem. In addition to sparsity, linear interpolation of elements from a large finite dictionary is considered among the conditions. Frequency estimation uncertainty is then limited only by signal-to-noise ratio (SNR), but the aproach is rather demanding from the computational viewpoint. In this paper a two-stage frequency estimation approach is presented. The first stage is a CS-based super-resolution algorithm, that provides the initial input to the second stage, where linear interpolation is carried out along the lines of CBP. Integration of the two steps into one effective algorithm requires some careful consideration of algorithm parameters, which is discussed in the following together with results obtained by simulation analysis.