Computationally efficient damped Capon and APES spectral estimation

In this paper, we introduce computationally efficient imple-
mentations of the data-dependent non-parametric damped
Capon (dCapon) and APES (dAPES) spectral estimators.
These estimators form two-dimensional frequency represen-
tations over both frequency and damping, and have been
shown to enable an efficient separation of closely spaced
spectral lines with different line widths. The proposed imple-
mentations are formed using an FFT-based fast polynomial
reformulation exploiting the displacement structure of the
matrices associated with the trigonometric polynomials that
appear in the nominator and the denominator of the spec-
tral estimators. The resulting implementations are exact and
notably reduces the required computational complexity of
the estimators. Numerical simulations illustrates the perfor-
mance and the achieved complexity gain of the proposed
implementations