# Reduction of Broadband Noise in Speech by Truncated QSVD

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## Abstract

1 Accurate Estimation of Low Fundamental Frequencies from Real-Valued Measurements Mads Græsbøll Christensen, Senior Member, IEEE Abstract— 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. INTRODUCTION Signals that are periodic can be decomposed into a sum of sinusoids having frequencies that are integer multiples of a fundamental frequency, much like the well-known Fourier series, except that real-life signals are noisy and are not observed over an integer number of periods. The problem of finding this fundamental frequency is referred to as funda- mental frequency estimation or sometimes as pitch estimation, with the latter term referring to the perceptual attribute that is associated with sound waves exhibiting periodicity. Many signals that can be encountered by the signal processing practitioner are periodic or approximately so. This is, for example, the case in speech processing, where voiced speech exhibits such characteristics, and in music processing for tones produced by musical instruments. Also in the analysis of some

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