On the probability of resolution for the amplitude and phase estimation (APES) spectral estimator

The amplitude and phase estimation (APES) algorithm is a spectral estimation approach that estimates the complex amplitude of the power spectrum of a random process. Although its resolution performance has been observed to be slightly better than conventional FFT approaches, but quite inferior to super-resolution approaches like the Capon algorithm and MUSIC, no quantitative measure of resolution exists for the APES algorithm. This analysis provides a new exact two point measure of the large sample probability of resolution for the APES algorithm, as well as an approximation useful in capturing finite sample effects. This probability measure indicates that the APES algorithm resolution performance is fundamentally limited even in the limit of infinite signal-to-noise ratio (SNR).