A super-resolution algorithm for multiband signal identification

Recent advances in convex optimization have led to super-resolution algorithms that provide exact frequency localization in multitone signals from limited time-domain samples. Such localization is accomplished by minimizing a certain atomic norm, which can be implemented in a semidefinite program. In this work, we consider the identification of multiband signals, which are comprised of multiple, unknown narrow bands of frequency content at multiple carrier frequencies. Integrating a basis of modulated discrete prolate spheroidal sequences (DPSS's) into the atomic norm minimization framework, we introduce a technique for estimating the unknown band positions based on limited time-domain samples of the signal.