Fast Fundamental Frequency Estimation: Making a Statistically Efficient Estimator Computationally Efficient

Speaker: Tobias Jensen
Affiliation: Aalborg University, Denmark

Abstract: Modelling signals as being periodic is common in many applications. Such periodic signals can be represented by a weighted sum of sinusoids with frequencies being an integer multiple of the fundamental frequency. Due to its widespread use, numerous methods have been proposed to estimate the fundamental frequency, and the maximum likelihood (ML) estimator is the most accurate estimator in pure statistical terms. When the noise is assumed to be white and Gaussian, the ML estimator is identical to the non-linear least squares (NLS) estimator. Despite being optimal in a statistical sense, the NLS estimator is considered to have a too high time complexity and to this end numerous suboptimal but computationally faster methods have been proposed over the years – in particular correlation based methods and the harmonic summation method. In this presentation, we propose an algorithm for lowering the time complexity of the NLS estimator significantly by showing that the objective function of the NLS estimator can be computed efficiently by solving two Toeplitz-plus-Hankel systems of equations and by exploiting recursive-in-order matrix structures of these systems. Specifically, the proposed algorithm reduces the time complexity to the same order as that of the harmonic summation method.

Biography: Tobias Jensen is a post-doc at Department of Electronic Systems, Aalborg University, Denmark. His research interests include optimization for signal processing, estimation and inverse problems.

For more information, contact Prof. Lieven Vandenberghe (vandenbe@ucla.edu)

Date/Time:
Date(s) - Mar 04, 2016
11:00 am - 12:00 pm

Location:
E-IV Maxwell Room #57-124
420 Westwood Plaza - 5th Flr. , Los Angeles CA 90095