Particle Filtering Applied to Musical Tempo Tracking
- PDF / 748,308 Bytes
- 11 Pages / 600 x 792 pts Page_size
- 74 Downloads / 189 Views
Particle Filtering Applied to Musical Tempo Tracking Stephen W. Hainsworth Department of Engineering, University of Cambridge, Cambridge CB2 1PZ, UK Email: [email protected]
Malcolm D. Macleod QinetiQ, Malvern, WR14 3PS, UK Email: [email protected] Received 30 May 2003; Revised 1 May 2004 This paper explores the use of particle filters for beat tracking in musical audio examples. The aim is to estimate the time-varying tempo process and to find the time locations of beats, as defined by human perception. Two alternative algorithms are presented, one which performs Rao-Blackwellisation to produce an almost deterministic formulation while the second is a formulation which models tempo as a Brownian motion process. The algorithms have been tested on a large and varied database of examples and results are comparable with the current state of the art. The deterministic algorithm gives the better performance of the two algorithms. Keywords and phrases: beat, tracking, particle filters, music.
1.
INTRODUCTION
Musical audio analysis has been a growing area for research over the last decade. One of the goals in the area is fully automated transcription of real polyphonic audio signals, though this problem is currently only partially solved. More realistic sub-tasks in the overall problem exist and can be explored with greater success; beat tracking is one of these and has many applications in its own right (automatic accompaniment of solo performances [1], auto-DJs, expressive rhythmic transformations [2], uses in database retrieval [3], metadata generation [4], etc.). This paper describes an investigation into beat tracking utilising particle filtering algorithms as a framework for sequential stochastic estimation where the state-space under consideration is a complex one and does not permit a closed form solution. Historically, a number of methods have been used to attempt solution of the problem, though they can be broadly categorised into a number of distinct methodologies.1 The oldest approach is to use oscillating filterbanks and to look for the maximum output; Scheirer [7] typifies this approach though Large [8] is another example. Autocorrelative methods have also been tried and Tzanetakis [3] or Foote [9] are 1A
comprehensive literature review can be found in Sepp¨anen [5] or Hainsworth [6].
examples, though these tend to only find the average tempo and not the phase (as defined in Section 2) of the beat. Multiple hypothesis approaches (e.g., Goto [10] or Dixon [11]) are very similar to more rigorously probabilistic approaches (Laroche [12] or Raphael [13], for instance) in that they all evaluate they likelihood of a hypothesis set; only the framework varies from case to case. Klapuri [14] also presents a method for beat tracking which takes the approach typified by Scheirer [7] and applies a probabilistic tempo smoothness model to the raw output. This is tested on an extensive database and the results are the current state of the art. More recently, particle filters have been applied to the problem;
Data Loading...
