1 Sektion Aalborg, The Faculty of Engineering and Science (ENG), Aalborg University, VBN2 Media Technology, The Faculty of Engineering and Science (ENG), Aalborg University, VBN3 Audio Analysis Lab, The Faculty of Engineering and Science (ENG), Aalborg University, VBN4 Department of Architecture, Design and Media Technology, The Faculty of Engineering and Science (ENG), Aalborg University, VBN5 The Faculty of Engineering and Science (TECH), Aalborg University, VBN
In this paper, the difficult problem of estimating low fundamental frequencies from real-valued measurements is addressed. The methods commonly employed do not take the phenomena encountered in this scenario into account and thus fail to deliver accurate estimates. The reason for this is that they employ asymptotic approximations that are violated when the harmonics are not well-separated in frequency, something that happens when the observed signal is real-valued and the fundamental frequency is low. To mitigate this, we analyze the problem and present some exact fundamental frequency estimators that are aimed at solving this problem. These esti- mators are based on the principles of nonlinear least-squares, harmonic fitting, optimal filtering, subspace orthogonality, and shift-invariance, and they all reduce to already published methods for a high number of observations. In experiments, the methods are compared and the increased accuracy obtained by avoiding asymptotic approximations is demonstrated.
I E E E Transactions on Audio, Speech and Language Processing, 2013, Vol 21, Issue 10, p. 2042-2056