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.
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About the Author(s)Mads Christensen
, Aalborg University, Denmark
Mads Christensen received his Ph.D. in 2005 from Aalborg University in Denmark, where he is also currently employed at the Department of Electronic Systems as Assistant Professor. He has been a visiting researcher at Philips Research Labs, Ecole Nationale Superieure des Telecommunications, Columbia University, and University of California Santa Barbara. Dr. Christensen has received several awards, namely an ICASSP Student Paper Award, the Spar Nord Foundation's Research Prize for his Ph.D. thesis, and a Danish Independent Research Council's Young Researcher's Award. His research interests include digital signal processing theory and methods with application to speech and audio, in particular parametric analysis, modeling, and coding.Andreas Jakobsson
, Lund University, Sweden
Andreas Jakobsson received his M.Sc. from Lund Institute of Technology and his Ph.D. in Signal Processing from Uppsala University in 1993 and 2000, respectively. Since, he has held positions with Global IP Sound AB, the Swedish Royal Institute of Technology, King's College London, and Karlstad University. He has also been a visiting researcher at King's College London, Brigham Young University, Stanford University, Katholieke Universiteit Leuven, and University of California, San Diego. He is currently Professor of Mathematical Statistics at Lund University, Sweden. He also holds an Honorary Research Fellowship at Cardiff University, UK. He is a Senior Member of IEEE, a member of the IEEE Sensor Array and Multichannel (SAM) Signal Processing Technical Committee, and an Associate Editor for the IEEE Transactions on Signal Processing, the IEEE Signal Processing Letters and the Research Letters in Signal Processing. His research interests include statistical and array signal processing, detection and estimation theory, and related application in remote sensing, telecommunication and biomedicine.