Multi-pitch estimation / Mads Græsbøll Christensen, Andreas Jakobsson.

Includes bibliographical references (p. 125-138) and index.

Fundamentals -- Introduction -- Related work -- Some applications -- Signal models -- Covariance matrix model -- Speech and audio signals -- Other signal models -- Parameter estimation bounds -- Evaluation of pitch estimators -- Statistical methods -- Introduction -- Maximum likelihood estimation -- Noise covariance matrix estimation -- White noise case -- Some maximum a posteriori estimators -- MAP model and order selection -- Fast multi-pitch estimation -- Expectation maximization -- Another related method -- Harmonic fitting -- Some results -- Discussion -- Filtering methods -- Introduction -- Comb filtering -- Filterbank interpretation of NLS -- Optimal filterbank design -- Optimal filter design -- Asymptotic analysis -- Inverse covariance matrix -- Variance and order estimation -- Fast implementation -- Some results -- Discussion -- Subspace methods -- Introduction -- Signal and noise subspace identification -- Subspace properties -- Pre-whitening -- Rank estimation using Eigenvalues -- Angles between subspaces -- Estimation using orthogonality -- Robust estimation -- Estimation using shift-invariance -- Some results -- Discussion -- Amplitude estimation -- Introduction -- Least squares estimation -- Capon- and APES-like amplitude estimates -- Some results and discussion -- The analytic signal -- Bibliography -- About the authors.

Periodic signals can be decomposed into sets of sinusoids having frequencies that are integer multiples of a fundamental frequency. The problem of finding such fundamental frequencies from noisy observations is important in many speech and audio applications, where it is commonly referred to as pitch estimation. These applications include analysis, compression, separation, enhancement, automatic transcription and many more. In this book, an introduction to pitch estimation is given and a number of statistical methods for pitch estimation are presented.The basic signal models and associated estimation theoretical bounds are introduced, and the properties of speech and audio signals are discussed and illustrated. The presented methods include both single- and multi-pitch estimators based on statistical approaches, like maximum likelihood and maximum a posteriori methods, filtering methods based on both static and optimal adaptive designs, and subspace methods based on the principles of subspace orthogonality and shift-invariance. The application of these methods to analysis of speech and audio signals is demonstrated using both real and synthetic signals, and their performance is assessed under various conditions and their properties discussed. Finally, the estimators are compared in terms of computational and statistical efficiency, generalizability and robustness.