Download Human Perception and Computer Extraction of Musical Beat Strength Musical signals exhibit periodic temporal structure that create the sensation of rhythm. In order to model, analyze, and retrieve musical signals it is important to automatically extract rhythmic information. To somewhat simplify the problem, automatic algorithms typically only extract information about the main beat of the signal which can be loosely defined as the regular periodic sequence of pulses corresponding to where a human would tap his foot while listening to the music. In these algorithms, the beat is characterized by its frequency (tempo), phase (accent locations) and a confidence measure about its detection. The main focus of this paper is the concept of Beat Strength, which will be loosely defined as one rhythmic characteristic that could allow to discriminate between two pieces of music having the same tempo. Using this definition, we might say that a piece of Hard Rock has a higher beat strength than a piece of Classical Music at the same tempo. Characteristics related to Beat Strength have been implicitely used in automatic beat detection algorithms and shown to be as important as tempo information for music classification and retrieval. In the work presented in this paper, a user study exploring the perception of Beat Strength was conducted and the results were used to calibrate and explore automatic Beat Strength measures based on the calculation of Beat Histograms.
Download Winding Numbers and Monodromy of Vector Bundles over a Circular Buffer The Möbius strip is perhaps the most recognizable topological object of general knowledge. It can be described mathematically in various ways including the formalism of line bundles. In this paper we discuss the bundle idea in the context of digital processing over a circular buffer and show how the idea leads to a more general notion known as monodromy, which describes the effect of the space on traversing a circle once. In this formulation, the monodromy of the Möbius strip is an orientation inversion characterized by a change in sign. This in turns leads to the concept of the winding number, which describes how many windings it takes to return to the original state. We discuss variable monodromy and illustrate that the winding number is robust under this variation. This will allow us to interpret previous disparate results in audio signal processing from Möbius waveguides to chaotic oscillators in delay loops in one unified framework. We close by showing how extending from line to vector bundles opens up the notion of braids to describe monodromy.