Alias-Suppressed Oscillators Based on Differentiated Polynomial Waveforms

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An efficient approach to the generation of classical synthesizer waveforms with reduced aliasing is proposed. This paper introduces two new classes of polynomial waveforms that can be differentiated one or more times to obtain an improved version of the sampled sawtooth and triangular signals. The differentiated polynomial waveforms (DPW) extend the previous differentiated parabolic wave method to higher polynomial orders, providing improved alias-suppression. Suitable polynomials of order higher than two can be derived either by analytically integrating a previous lower order polynomial or by solving the polynomial coefficients directly from a set of equations based on constraints. We also show how rectangular waveforms can be easily produced by differentiating a triangular signal. Bandlimited impulse trains can be obtained by differentiating the sawtooth or the rectangular signal. An objective evaluation using masking and hearing threshold models shows that a fourth-order DPW method is perceptually alias-free over the whole register of the grand piano. The proposed methods are applicable in digital implementations of subtractive sound synthesis.
Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
Issue Date
2010-05
Language
English
Article Type
Article
Keywords

ANALOG SYNTHESIS

Citation

IEEE TRANSACTIONS ON AUDIO SPEECH AND LANGUAGE PROCESSING, v.18, no.4, pp.786 - 798

ISSN
1558-7916
DOI
10.1109/TASL.2009.2026507
URI
http://hdl.handle.net/10203/201417
Appears in Collection
GCT-Journal Papers(저널논문)
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