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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 |
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Keywords: | timbre, pitch, identification, harmonic, phase, Fourier |
Research Division: | Engineering |
Research Group: | Engineering practice and education |
Research Field: | Engineering practice and education not elsewhere classified |
Objective Division: | Expanding Knowledge |
Objective Group: | Expanding knowledge |
Objective Field: | Expanding knowledge in engineering |
UTAS Author: | Holloway, D (Associate Professor Damien Holloway) |
ID Code: | 93107 |
Year Published: | 2014 |
Deposited By: | Engineering |
Deposited On: | 2014-07-12 |
Last Modified: | 2015-03-20 |
Downloads: | 0 |
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