An optimization theoretic framework for spectral estimation

We present an optimization theoretic framework for spectral estimation. A theorem is given which provides a unification of several prevalent estimates and gives us the ability to systematically generate new classes of estimators. As one application a new optimal estimate was derived, tailored to smooth bandlimited spectra. A fast polynomial recursion exists for computing this estimate, and an extension makes it suitable for data consisting of sinusoids and noise. The high performance of this new estimate is indicative of the effectiveness of the proposed optimization techniques.