Recursive and Fast Recursive Capon Spectral Estimators
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Research Article Recursive and Fast Recursive Capon Spectral Estimators Jacob Benesty,1 Jingdong Chen,2 and Yiteng (Arden) Huang2 1 Universit´ e 2 Bell
du Qu´ebec, INRS-EMT, 800 de la Gaucheti`ere Ouest, Suite 6900, Montr´eal, Qu´ebec, Canada H5A 1K6 Laboratories, Alcatel-Lucent , 600 Mountain Avenue, Murray Hill, NJ 07974, USA
Received 26 April 2006; Revised 13 November 2006; Accepted 11 December 2006 Recommended by Ulrich Heute The Capon algorithm, which was originally proposed for wavenumber estimation in array signal processing, has become a powerful tool for spectral analysis. Over several decades, a significant amount of research attention has been devoted to the estimation of the Capon spectrum. Most of the developed algorithms thus far, however, rely on the direct computation of the inverse of the input correlation (or covariance) matrix, which can be computationally very expensive particularly when the dimension of the matrix is large. This paper deals with fast and efficient algorithms in computing the Capon spectrum. Inspired from the recursive idea established in adaptive signal processing theory, we first derive a recursive Capon algorithm. This new algorithm does not require an explicit matrix inversion, and hence it is more efficient to implement than the direct-inverse approach. We then develop a fast version of the recursive algorithm based on techniques used in fast recursive least-squares adaptive algorithms. This new fast algorithm can further reduce the complexity of the recursive Capon algorithm by an order of magnitude. Although our focus is on the Capon spectral estimation, the ideas shown in this paper can also be generalized and applied to other applications. To illustrate this, we will show how to apply the recursive idea to the estimation of the magnitude squared coherence function, which plays an important role for problems like time-delay estimation, signal-to-noise ratio estimation, and doubletalk detection in echo cancellation. Copyright © 2007 Jacob Benesty et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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INTRODUCTION
Spectral estimation, which endeavors to determine the spectral content of a signal from a finite set of measurements, plays a major role in signal processing. It has a wide variety of applications in diversified fields such as radar, sonar, speech, communications, to name a few. Over the last century, a significant amount of research attention has been devoted to developing techniques for high performance spectral estimation. Some good reviews of such efforts can be found in [1– 3]. Broadly, the developed techniques can be classified into two categories: nonparametric and parametric methods. The former is based on the concept of bandpass filtering. The latter assumes a model for the data, and the spectral estimation is then formulated into a problem of estimating the parameters in the assumed mod
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