Multiple F 0 Estimation

This chapter is about the estimation of multiple fundamental frequencies (F0) from a waveform such as the compound sound of several people speaking at the same time, or several musical instruments playing together. That information may be needed to transcribe the music to a score, to extract intonation patterns for speech recognition, or as an ingredient for computational auditory scene analysis. The task of estimating the single F0 of an isolated voice has motivated a surprising amount of effort over the years [45]. Work on the harder task of estimating multiple F0s is now gaining momentum, fueled by progress in signal processing techniques on the one hand, and new applications such as interactive processing or indexing of music, multimedia and speech on the other. A multiple F0 estimation method is typically assembled from two elements: a singlevoice F0 estimator, and a voice-segregation scheme. Here “voice” is used in a wide sense to designate the periodic signal produced by a source (human voice, instrument sound, etc.). Some space is accordingly devoted the topic single voice F0 estimation, but the reader should refer to the excellent treatise of Hess [45] for more details. Segregation techniques too are evoked, but the reader should follow pointers to other chapters of this book wherever possible. A sound with a periodic waveform evokes a pitch that varies with F0, the inverse of the period [87]. The pitch may be salient and musical as long as the F0 is within about 30