Beat Tracking using an Autocorrelation Phase Matrix

We introduce a novel method for estimating beat from digital audio. We compute autocorrelation such that the distribution of energy in phase space is preserved in a so-called autocorrelation phase matrix (APM). We estimate beats by computing individual APMs over short overlapping segments of an onset trace derived from the audio. Then an adaptation of Viterbi decoding is used to search the APMs for metrical combinations of points that change smoothly over time in the lag/phase plane. Because small temporal perturbations are seen as local movements on the APM, the Viterbi search can be bounded using a small 2D Gaussian window. The resulting algorithm jointly estimates tempo, meter and beat. As is always the case with Viterbi decoding, an online version is possible although best performance is achieved offline. We report results on an annotated dataset of 60-second musical segments.