Fast and statistically efficient fundamental frequency estimation

Abstract

Fundamental frequency estimation is a very important task in many applications involving periodic signals. For computational reasons, fast autocorrelation-based estimation methods are often used despite parametric estimation methods having superior estimation accuracy. However, these parametric methods are much more costly to run. In this paper, we propose an algorithm which significantly reduces the computational cost of an accurate maximum likelihood-based estimator for real-valued data. The computational cost is reduced by exploiting the matrix structure of the problem and by using a recursive solver. Via benchmarks, we demonstrate that the computation time is reduced by approximately two orders of magnitude. The proposed fast algorithm is available for download online.

Fast fundamental frequency estimation: Making a statistically efficient estimator computationally efficient

“…We have previously outlined these ideas in [14], but we here give a much more detailed description of how the time complexity is reduced. This reduction is based on five key 185 facts which are described in the following five sections.…”

“…Unfortunately, they have a suboptimal estimation performance, are not very robust to noise (see, e.g., Fig. 3), and do not work for low fundamental frequencies [14]. Here, a low frequency means the number of cycles in a segment of data rather than the frequency 40 measured in, e.g., Hz or radians/s, and this also explains the somewhat non-standard value on the x-axis in Fig.…”

A Study on How Pre-whitening Influences Fundamental Frequency Estimation

“…A signal model which takes into account the noise presence can be used to derive a parametric estimator [9], based on statistical assumptions. Recently, a fast algorithm which considerably reduces the computational complexity of a nonlinear least squares (NLS) estimator has been proposed [8,10]. This NLS fundamental frequency estimator is only statistically efficient under a white Gaussian noise (WGN) condition.…”

Estimating acoustic speech features in low signal-to-noise ratios using a statistical framework

“…However, these methods are generally inaccurate in low noise conditions and when estimating low fundamental frequencies (Nielsen et al, 2016). Noiserobust non-parametric methods include XAFE and PEFAC (ETSI, 2003;Gonzalez and Brookes, 2014).…”

“…Parametric methods employ a model of the noisy speech signal with one of its parameters being fundamental frequency (although other parameters such as the amplitudes and phases of the harmonics can also be included in the parameter set). An estimate of the model parameters is then made from the noisy signal using, for example, maximum likelihood (ML), non-linear least squares (NLS) and weighted least squares (WLS) methods (Christensen and Jakobsson, 2009;Li et al, 2000;Nielsen et al, 2016).…”