Theses and Dissertations
This collection includes both ASU Theses and Dissertations, submitted by graduate students, and the Barrett, Honors College theses submitted by undergraduate students.
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- Creators: Turaga, Pavan
Description
The tradition of building musical robots and automata is thousands of years old. Despite this rich history, even today musical robots do not play with as much nuance and subtlety as human musicians. In particular, most instruments allow the player to manipulate timbre while playing; if a violinist is told to sustain an E, they will select which string to play it on, how much bow pressure and velocity to use, whether to use the entire bow or only the portion near the tip or the frog, how close to the bridge or fingerboard to contact the string, whether or not to use a mute, and so forth. Each one of these choices affects the resulting timbre, and navigating this timbre space is part of the art of playing the instrument. Nonetheless, this type of timbral nuance has been largely ignored in the design of musical robots. Therefore, this dissertation introduces a suite of techniques that deal with timbral nuance in musical robots. Chapter 1 provides the motivating ideas and introduces Kiki, a robot designed by the author to explore timbral nuance. Chapter 2 provides a long history of musical robots, establishing the under-researched nature of timbral nuance. Chapter 3 is a comprehensive treatment of dynamic timbre production in percussion robots and, using Kiki as a case-study, provides a variety of techniques for designing striking mechanisms that produce a range of timbres similar to those produced by human players. Chapter 4 introduces a machine-learning algorithm for recognizing timbres, so that a robot can transcribe timbres played by a human during live performance. Chapter 5 introduces a technique that allows a robot to learn how to produce isolated instances of particular timbres by listening to a human play an examples of those timbres. The 6th and final chapter introduces a method that allows a robot to learn the musical context of different timbres; this is done in realtime during interactive improvisation between a human and robot, wherein the robot builds a statistical model of which timbres the human plays in which contexts, and uses this to inform its own playing.
ContributorsKrzyzaniak, Michael Joseph (Author) / Coleman, Grisha (Thesis advisor) / Turaga, Pavan (Committee member) / Artemiadis, Panagiotis (Committee member) / Arizona State University (Publisher)
Created2016
Recursive Bayesian Estimation on Projective Spaces: Theoretical Foundations and Practical Algorithms
Description
This thesis develops geometrically and statistically rigorous foundations for multivariate analysis and bayesian inference posed on grassmannian manifolds. Requisite to the development of key elements of statistical theory in a geometric realm are closed-form, analytic expressions for many differential geometric objects, e.g., tangent vectors, metrics, geodesics, volume forms. The first part of this thesis is devoted to a mathematical exposition of these. In particular, it leverages the classical work of Alan James to derive the exterior calculus of differential forms on special grassmannians for invariant measures with respect to which integration is permissible. Motivated by various multi-sensor remote sensing applications, the second part of this thesis describes the problem of recursively estimating the state of a dynamical system propagating on the Grassmann manifold. Fundamental to the bayesian treatment of this problem is the choice of a suitable probability distribution to a priori model the state. Using the Method of Maximum Entropy, a derivation of maximum-entropy probability distributions on the state space that uses the developed geometric theory is characterized. Statistical analyses of these distributions, including parameter estimation, are also presented. These probability distributions and the statistical analysis thereof are original contributions. Using the bayesian framework, two recursive estimation algorithms, both of which rely on noisy measurements on (special cases of) the Grassmann manifold, are the devised and implemented numerically. The first is applied to an idealized scenario, the second to a more practically motivated scenario. The novelty of both of these algorithms lies in the use of thederived maximumentropy probability measures as models for the priors. Numerical simulations demonstrate that, under mild assumptions, both estimation algorithms produce accurate and statistically meaningful outputs. This thesis aims to chart the interface between differential geometry and statistical signal processing. It is my deepest hope that the geometric-statistical approach underlying this work facilitates and encourages the development of new theories and new computational methods in geometry. Application of these, in turn, will bring new insights and bettersolutions to a number of extant and emerging problems in signal processing.
ContributorsCrider, Lauren N (Author) / Cochran, Douglas (Thesis advisor) / Kotschwar, Brett (Committee member) / Scharf, Louis (Committee member) / Taylor, Thomas (Committee member) / Turaga, Pavan (Committee member) / Arizona State University (Publisher)
Created2021