Spectral estimation via minimum energy correlation extension

It is well known that the Discrete Fourier Transform of a truncated correlation sequence (the Blackman-Tukey estimate) can become negative at certain frequencies. Since the true power spectrum must, in fact, be positive, negative estimates are undesirable. In this paper, we obtain the positive spectral estimate which is as close to the Blackman-Tukey estimate as possible (in L2norm) while still matching the correlation constraints. In the time domain, this estimate yields the correlation extension of least energy for the specified truncated correlation sequence. Algorithms and numerical examples will be provided. Multidimensional minimum energy correlation extension is discussed. In multidimensions, the minimum energy estimate is shown to exist in certain cases when the autoregressive maximum entropy estimate fails to exist.