Chapter 7: Statistical Models

The search for rhythmic patterns can take many forms. Models of statistical periodicity do not presume that the signal itself is periodic; rather, they assume that there is a periodicity in the underlying statistical distributions. In some cases, the randomness is locked to a known periodic grid on which the statistics are defined. In other cases, the random fluctuations may be synchronized to a grid with unknown period. In still other cases, the underlying rate or period of the repetition may itself change over time. The statistical methods relate the signal (for example, a musical performance) to the probability distribution of useful parameters such as the period and phase of a repetitive phenomenon. These form the backbone of the beat tracking system that will be used throghout the remainder of Rhythm and Transforms.

7.1  Probability and Inference
7.2  Statistical Models of Periodic Phenomenon
7.3  Regularities in Binary Sequences
7.4  A Model for Symbolic Pulse Detection
7.5  A Model for Symbolic Pulse Tracking
7.6  A Model for Audio Feature Vectors