We devise novel, interpolation-free, and computationally tractable extensions of the spectral analysis methods Capon and APES (amplitude and phase estimation) to periodically gapped data. Our methods are based on the observation that periodically gapped data usually have a structure that supports estimation of a relatively large number of covariance lags. The large signal-to-noise-ratio (SNR) behavior of the new algorithms is discussed, and numerical examples are provided to illustrate their performance.
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