The spectrum analysis problem based on the periodogram and Capon estimates from a nonuniformly sampled signal is addressed. The nonuniform sampling process is cast as a linear projection matrix which encompasses several recent sampling strategies such as compressive sampling. A rank-1 correlation-matching approach is proposed to derive a general filter-bank framework that allows the formulation of the nonuniform periodogram and Capon estimates as particular cases. The performance of the novel periodogram and Capon estimates is analyzed in a cognitive radio scenario where the primary system is a multiband signal with sparse spectrum. Both theoretical and numerical results show that the denoising process required by correlation-matching plays an important role in spectral analysis based on nonuniform sampling.

Peer Reviewed