High temporal resolution estimators through reduced rank periodograms

The kernel associated with positive estimators including the periodograms is expressed as a linear combination of separable kernels, each defining a smoothed pseudo-Wigner distribution (SPWD). This is achieved by applying the singular value decomposition to the two-dimensional kernel matrix in time and lag variables. The SPWD corresponding to the maximum singular value is considered the rank one kernel estimator that is the closest to the full rank kernel periodogram. Error bounds are derived, and simulations are performed to demonstrate the effect of limiting the decomposition of the kernel matrix to dominant singular values