1 Department of Architecture, Design and Media Technology, The Technical Faculty of IT and Design, Aalborg University, VBN2 Audio Analysis Lab, The Technical Faculty of IT and Design, Aalborg University, VBN3 The Faculty of Engineering and Science (TECH), Aalborg University, VBN4 Sektion Aalborg, The Technical Faculty of IT and Design, Aalborg University, VBN5 Media Technology, The Technical Faculty of IT and Design, Aalborg University, VBN6 Department of Electronic Systems, The Technical Faculty of IT and Design, Aalborg University, VBN7 Signal and Information Processing, The Technical Faculty of IT and Design, Aalborg University, VBN8 Multimedia Information and Signal Processing, The Technical Faculty of IT and Design, Aalborg University, VBN9 Dept. of Science and Technology of Telecommunications, University of Peloponnese10 Dept. of Mathematical Statistics, Lund University
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 LCMV-based fundamental frequency estimators, exploiting the estimators' inherently low displacement rank of the used Toeplitz-like 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 IAA-based data covariance matrix estimator, reminiscent of the recently proposed Quasi-Newton IAA technique. Furthermore, it is shown how the considered pitch estimators can be efficiently updated when new observations become available. The resulting time-recursive 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 time-recursive implementations are able to track pitch fluctuations of synthetic as well as real-life signals.
I E E E Transactions on Signal Processing, 2013, Vol 61, Issue 12, p. 3159-3172
data adaptive estimators; efficient algorithms; Fundamental frequency estimation; optimal filtering