Article
IAA Spectral Estimation: Fast Implementation Using the Gohberg–Semencul Factorization
Dept. of Electr. & Comput. Eng., Univ. of Florida, Gainesville, FL, USA
IEEE Transactions on Signal Processing (Impact Factor: 2.81). 08/2011; DOI: 10.1109/TSP.2011.2131136 Source: DBLP

Article: Extended Fourier analysis of signals
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ABSTRACT: This extended summary of Dr.Sc.Comp. thesis is created to emphasis the tight connection of the proposed spectral analysis method with the Discrete Fourier Transform (DFT)  the most extensively studied and frequently used approach in the history of signal processing. It is shown that in a typical application case, where uniform data readings are transformed to the same number of uniformly spaced frequencies, the results of the classical DFT and proposed approach coincide. The difference in performance appears when the length of the DFT is selected to be greater than the length of the data. The DFT solves the unknown data problem by padding readings with zeros up to the length of the DFT, while the proposed Extended DFT (EDFT) deals with this situation in a different way, it uses the Fourier integral transform as a target and optimizes the transform basis in the extended frequency range without putting such restrictions on the time domain. Thus, the Inverse DFT (IDFT) applied to the result of EDFT returns not only known readings but also the extrapolated data, where classical DFT is able to give back just zeros. The EDFT significantly extends the usability of the DFT based methods, where previously these approaches were considered inapplicable. The EDFT founds the solution in an iterative way and requires repeated calculations to get the adaptive basis, and this makes its numerical complexity much higher compared to DFT. This disadvantage was a serious problem in 1990s, when the method has been proposed. Fortunately, since then the power of computers has increased so much that nowadays EDFT application could be considered as a real alternative.03/2013;  [Show abstract] [Hide abstract]
ABSTRACT: Recently, optimal linearly constrained minimum variance (LCMV) filtering methods have been applied to fundamental frequency estimation. Such estimators often yield preferable performance but suffer from being computationally cumbersome as the resulting cost functions are multimodal with narrow peaks and require matrix inversions for each point in the search grid. In this paper, we therefore consider fast implementations of LCMVbased fundamental frequency estimators, exploiting the estimators' inherently low displacement rank of the used Toeplitzlike data covariance matrices, using as such either the classic time domain averaging covariance matrix estimator, or, if aiming for an increased spectral resolution, the covariance matrix resulting from the application of the recent iterative adaptive approach (IAA). The proposed exact implementations reduce the required computational complexity with several orders of magnitude, but, as we show, further computational savings can be obtained by the adoption of an approximative IAAbased data covariance matrix estimator, reminiscent of the recently proposed QuasiNewton IAA technique. Furthermore, it is shown how the considered pitch estimators can be efficiently updated when new observations become available. The resulting timerecursive updating can reduce the computational complexity even further. The experimental results show that the performances of the proposed methods are comparable or better than that of other competing methods in terms of spectral resolution. Finally, it is shown that the timerecursive implementations are able to track pitch fluctuations of synthetic as well as reallife signals.IEEE Transactions on Signal Processing 01/2013; 61(12):31593172. · 2.81 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: The development of highresolution twodimensional spectral estimation techniques is of notable interest in synthetic aperture radar (SAR) imaging. Typically, dataindependent techniques are exploited to form the SAR images, although such approaches will suffer from limited resolution and high sidelobe levels. Recent work on dataadaptive approaches have shown that both the iterative adaptive approach (IAA) and the sparse learning via iterative minimization (SLIM) algorithm offer excellent performance with highresolution and low side lobe levels for both complete and incomplete data sets. Regrettably, both algorithms are computationally intensive if applied directly to the phase history data to form the SAR images. To help alleviate this, efficient implementations have also been proposed. In this paper, we further this work, proposing yet further improved implementation strategies, including approaches using the segmented IAA approach and the approximative quasiNewton technique. Furthermore, we introduce a combined IAAMAP algorithm as well as a hybrid IAA and SLIMbased estimation scheme for SAR imaging. The effectiveness of the SAR imaging algorithms and the computational complexities of their fast implementations are demonstrated using the simulated Slicy data set and the experimentally measured GOTCHA data set.IEEE Transactions on Signal Processing 04/2013; 61(7):16141624. · 2.81 Impact Factor
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