Computationally efficient damped Capon and APES spectral estimation

In this paper, we introduce computationally efficient implementations of the data-dependent non-parametric damped Capon (dCapon) and APES (dAPES) spectral estimators. These estimators form two-dimensional frequency representations 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 implementations 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 spectral estimators. The resulting implementations are exact and notably reduces the required computational complexity of the estimators. Numerical simulations illustrates the performance and the achieved complexity gain of the proposed implementations.