Perceptually informed synthesis of bandlimited classical waveforms using integrated polynomial interpolation

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Digital subtractive synthesis is a popular music synthesis method, which requires oscillators that are aliasing-free in a perceptual sense. It is a research challenge to find computationally efficient waveform generation algorithms that produce similar-sounding signals to analog music synthesizers but which are free from audible aliasing. A technique for approximately bandlimited waveform generation is considered that is based on a polynomial correction function, which is defined as the difference of a non-bandlimited step function and a polynomial approximation of the ideal bandlimited step function. It is shown that the ideal bandlimited step function is equivalent to the sine integral, and that integrated polynomial interpolation methods can successfully approximate it. Integrated Lagrange interpolation and B-spline basis functions are considered for polynomial approximation. The polynomial correction function can be added onto samples around each discontinuity in a non-bandlimited waveform to suppress aliasing. Comparison against previously known methods shows that the proposed technique yields the best tradeoff between computational cost and sound quality. The superior method amongst those considered in this study is the integrated third-order B-spline correction function, which offers perceptually aliasing-free sawtooth emulation up to the fundamental frequency of 7.8 kHz at the sample rate of 44.1 kHz. (C) 2012 Acoustical Society of America. [DOI: 10.1121/1.3651227]
Publisher
ACOUSTICAL SOC AMER AMER INST PHYSICS
Issue Date
2012-01
Language
English
Article Type
Article
Keywords

ANALOG SYNTHESIS; SOUND SYNTHESIS; OSCILLATORS; ALGORITHMS; FORMULAS; SPECTRA; FILTER; SIGNAL; DELAY

Citation

JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA, v.131, no.1, pp.974 - 986

ISSN
0001-4966
DOI
10.1121/1.3651227
URI
http://hdl.handle.net/10203/201388
Appears in Collection
GCT-Journal Papers(저널논문)
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