@PHDTHESIS{Davies2007thesis,
   author = {Matthew Davies},
   title = {Towards Automatic Rhythmic Accompaniment},
   school = {Queen Mary University of London},
   address = {London, UK},
   month = {August},
   year = {2007},
   url = {http://www.elec.qmul.ac.uk/digitalmusic/papers/2007/Davies07-phdthesis.pdf},
   abstract = {
       In this thesis we investigate the automatic extraction of rhythmic and metrical information from audio signals. Primarily we address three analysis tasks: the extraction of beat times, equivalent to the human ability of foot-tapping in time to music; finding bar boundaries, which can be considered analogous to counting the beats of the bar; and thirdly the extraction of a predominant rhythmic pattern to characterise the distribution of note onsets within the bars.
       
       We extract beat times from an onset detection function using a two-state beat tracking model. The first state is used to discover an initial tempo and track tempo changes, while the second state maintains contextual continuity within consistent tempo hypotheses. The bar boundaries are recovered by finding the spectral difference between beat synchronous analysis frames, and the predominant rhythmic pattern by clustering bar length onset detection function frames.
       
       In addition to the new techniques presented for extracting rhythmic information, we also address the problem of evaluation, that of how to quantify the extent to which the analysis has been successful. To this aim we propose a new formulation for beat tracking evaluation, where accuracy is measured in terms of the entropy of a beat error histogram.
       
       To illustrate the combination of all three layers of analysis we present this research in the context of automatic musical accompaniment, such that the resulting rhythmic information can be realised as an automatic percussive accompaniment to a given input audio signal.
   }
}