eCite Digital Repository

Accurate temporal resolution of harmonic content in both amplitude and phase

Citation

Holloway, D, Accurate temporal resolution of harmonic content in both amplitude and phase, ANZIAM Journal, 1-4 December 2013, Brisbane, Australia, pp. C235-C249. ISSN 1446-8735 (2014) [Refereed Conference Paper]

Copyright Statement

Copyright 2014 Austral. Mathematical Society

Official URL: http://journal.austms.org.au/ojs/index.php/ANZIAMJ...

Abstract

Frequency content of a periodic signal is easily computed using fast Fourier transforms (FFT). While the magnitude is well predicted, phase information is usually meaningless and temporal changes are difficult to resolve accurately over short time periods, even with techniques such as discrete time Fourier transforms or wavelets. These problems arise in the analysis of musical sounds and should be solvable since a well trained human ear can detect subtle and rapid changes to timbre and pitch that occur with expressiveness, techniques such as ‘vibrato’, and lack of tone control exhibited by music students. Starting with the premise that a musical sound is truly periodic, we obtain much more accurate information from a Fourier series than from a Fourier transform. In this article the Fourier series of a periodic signal is evaluated using a least squares fit, as was done before the popularisation of the FFT algorithm, but the difference is that the frequency is precisely defined before fitting the coefficients, which succeeds with as few as three or four cycles. The proposed technique achieves the above objectives and opens up the possibility of exploring the role of phase in the quantification of musical sound, a critical component that is traditionally ignored.

Item Details

Item Type:Refereed Conference Paper
Keywords:timbre, pitch, identification, harmonic, phase, Fourier
Research Division:Engineering
Research Group:Interdisciplinary Engineering
Research Field:Interdisciplinary Engineering not elsewhere classified
Objective Division:Expanding Knowledge
Objective Group:Expanding Knowledge
Objective Field:Expanding Knowledge in Engineering
Author:Holloway, D (Dr Damien Holloway)
ID Code:93107
Year Published:2014
Deposited By:Engineering
Deposited On:2014-07-12
Last Modified:2015-03-20
Downloads:0

Repository Staff Only: item control page