Principal component separation in sparse signal recovery for harmonic retrieval

Methods for best basis selection (BBS) can be used to address the problem of harmonic retrieval using a large basis of harmonically related complex sinusoids with an iterative reweighted BBS method. This approach produces a data-consistent representation with a maximally sparse set of non-zero expansion coefficients. The method is modified to accommodate the presence of additive white noise by the application of principal component separation or SVD truncation. Using computer simulations for a classic example involving two closely spaced complex sinusoids, we illustrate the properties and performance of this frequency estimator in comparison to its predecessor, the adaptive extrapolation method. Over a limited range of low SNR values, the method performs better than many of the established harmonic retrieval techniques, despite the presence of an estimation bias.