ABSTRACT:
Autocorrelation is a simple, fast-to-compute statistical method that has long been used to discover metrical structure in music (e.g. Judy Brown, 1993). Because autocorrelation can be performed online and works on any time series, it is a promising method for detecting temporal regularities in music. However autocorrelation has a significant limitation: while it provides the relative magnitude of signal energy at different periods, it discards all information about phase. Furthermore, autocorrelation does not tend to work well for vocals and for non-percussive musical instruments such as strings. I provide a short analysis of these limitations and address them by offering a relatively fast method that computes a "phase-preserving" autocorrelation. The resulting phase-by-period matrix provides information relevant for tempo tracking and for meter prediction as well as for related tasks such as beat induction. In this talk I will focus on how a (Shannon) entropy analysis of phase information can significantly enhance an autocorrelation-based measure of tempo and meter. This approach works well on vocal and non-percussive music. Furthermore it achieves good performance without complex pre-processing, operating directly on the absolute value of a 1Khz-sampled digital audio signal. I will present simulation results for tempo tracking and for meter prediction. I will conclude by observing that the model performs a particularly useful dimensionality reduction on digital audio and can perhaps aid in more complex musical learning tasks such as automatic music composition.
Douglas Eck: Entropy and Autocorrelation: Using Simple Statistics to Find Tempo and Metrical Structure in Unfiltered Digital Audio
Doug Eck is an assistant professor in the Department of Computer Science, University of Montreal. His work concerns the processing and learning of temporal patterns such as music and speech.
March 18, 2005
15:45 - 17:00