1], sonar [2], geophysics [3], biomedical signal pro-Kiernan, P., Two-Dimensional Spectral Estimation by cessing [4], radar [5], and radio astronomy [6]. As Free Energy Minimization, Digital Signal Processing 6 stated in [7], ''the operation of spectral analysis (1996), 160-168. arises in many fields of application. Situations in which signals are inherently multidimensional can
We present a high-resolution 2-D minimum free energy be found in geophysics, radio astronomy, sonar, and (MFE) spectral estimation technique which is a 2-D extenradar, to mention a few. These multidimensional sion of the MFE spectral estimation method. We demonproblems present a challenging set of theoretical and strate the performance of the technique for spectral estimation of closely spaced 2-D sinusoids in white Gaussian computational difficulties that must be tackled.'' noise. Results from our tests on the effect of signal pro-These areas will benefit from continuing advances cessing temperature illustrate that our method provides in spectral estimation [8].
accurate low model order autoregressive spectral estima-As stated in [9], ''digital spectral estimation contion. The method provides superior spectral estimation tinues to be an active area of research for better with similar computational burden to that achieved with estimation methods and faster computational algothe Levinson algorithm for a number of cases involving rithms.'' The search continues for an efficient highsinusoids in white noise at various signal-to-noise ratio resolution multidimensional parametric spectral es-(SNR) levels. An example is provided. The method is timation technique that is computationally efficient faster than the modified covariance method (MCV). An and capable of operating with small data sets and example is given from a number of cases involving two at low signal-to-noise ratio (SNR). Furthermore the closely spaced sinusoids at low SNR, where MFE estiefficiency and high resolution of 1-D techniques mates are as well resolved as MCV estimates. MFE models may also be used for correlation extension and for field make extension of these techniques to 2-D an attracmodeling and synthesis. We indicate possible extensions tive option.
to the MFE method for computational efficiency improve-A high resolution quarter plane (QP) autoregresment, a priori temperature determination, and the use of sive (AR) spectral estimation method is presented. higher-order statistics.