Date of Submission

Spring 2018

Academic Programs and Concentrations

Mathematics

Project Advisor 1

Matthew Deady

Project Advisor 2

Matthew Sargent

Abstract/Artist's Statement

Analog audio implies time-frequency dependence. With digitally sampled audio, this timefrequency dependence can be broken and either variable can be manipulated independently of the other, in real time. This paper will mostly focus on the frequency domain algorithm called the Phase Vocoder which breaks this time-frequency dependence. We will start by looking at Fourier Theory and the effect of discrete sampling. Then we will look at the Phase Vocoder's theory of operation, as well as improvements made by Puckette, Laroche, and Dolson, to name a few. Through all of this, simple examples will be presented in order to gain intuition into the principles at hand. Towards the end, a time domain approach for time-frequency independence called Granular Synthesis will be explored. We will compare it to the Phase Vocoder, and see how our understanding of one changes how we think and make decisions for the other. Finally we will propose some ideas for further improvement to real-time time-frequency independent manipulation of audio.

Open Access Agreement

Open Access

Creative Commons License

Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

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