Alexandria Digital Research Library

The Harmonic Pattern Function: A Mathematical Model Integrating Synthesis of Sound and Graphical Patterns

Author:
Putnam, Lance Jonathan
Degree Grantor:
University of California, Santa Barbara. Media Arts and Technology
Degree Supervisor:
JoAnn Kuchera-Morin
Place of Publication:
[Santa Barbara, Calif.]
Publisher:
University of California, Santa Barbara
Creation Date:
2011
Issued Date:
2011
Topics:
Applied Mathematics, Multimedia Communications, and Engineering, Electronics and Electrical
Keywords:
Sound synthesis
Graphics
Harmonics
Patterns
Digital signal processing
Audiovisual
Genres:
Dissertations, Academic and Online resources
Dissertation:
Ph.D.--University of California, Santa Barbara, 2011
Description:

The current landscape of parametric techniques for synthesis of digital sound waveforms and graphical curves and shapes is vast, but is largely an incongruous mixture of closed and highly specialized mathematical equations. While much of this can be attributed to the independent development of synthesis techniques within each field, upon closer examination it is clear that there exist common mathematical bases between the modalities. By pulling back into a broader mathematical context, it is possible to develop a language of unified audio/visual synthesis principles so that many of the existing paradigms, regardless of modality, can be understood from a single vantage point.

This dissertation defends the thesis that a large portion of known sound and graphical synthesis techniques can be unified through a rational function of inverse discrete Fourier transforms and that symmetry, invariance under transformation, plays an important role in understanding the patterns that it produces. We call this newly proposed audio/visual synthesis model the harmonic pattern function. A survey of a wide assortment of historic mechanical and electronic devices and computational systems used for generating sonic and visual patterns in art and science reveals that their underlying mathematical descriptions are special cases of this new synthesis function.

The contributions of this dissertation include the introduction of a simple mathematical function, the harmonic pattern function, capable of generating a wide assortment of both known and previously unknown patterns useful for sound and/or visual synthesis, a simplified notation for specifying the complex sinusoids composing such patterns, and a thorough analysis of general themes and specific instances of patterns producible from the harmonic pattern function.

Physical Description:
1 online resource (236 pages)
Format:
Text
Collection(s):
UCSB electronic theses and dissertations
ARK:
ark:/48907/f3bz63zm
ISBN:
9781267294814
Catalog System Number:
990037519100203776
Rights:
Inc.icon only.dark In Copyright
Copyright Holder:
Lance Putnam
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