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Perceptually informed synthesis of bandlimited classical waveforms using integrated polynomial interpolation.

Vesa Välimäki1, Jussi Pekonen, Juhan Nam

  • 1Department of Signal Processing and Acoustics, Aalto University, Espoo, Finland. vesa.valimaki@tkk.fi

The Journal of the Acoustical Society of America
|January 28, 2012
PubMed
Summary

This study introduces a new digital synthesis method using polynomial correction functions to eliminate audible aliasing in music oscillators. The integrated third-order B-spline method offers the best balance of computational efficiency and sound quality for aliasing-free waveforms.

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Area of Science:

  • Digital Signal Processing
  • Music Synthesis
  • Computational Audio

Background:

  • Digital subtractive synthesis requires aliasing-free oscillators for high-quality sound.
  • Achieving perceptually aliasing-free waveforms with computational efficiency remains a challenge.

Purpose of the Study:

  • To develop and evaluate a computationally efficient waveform generation technique for digital music synthesizers.
  • To minimize audible aliasing in synthesized audio signals.

Main Methods:

  • A polynomial correction function was designed as the difference between a non-bandlimited and an approximated bandlimited step function.
  • Integrated polynomial interpolation, including Lagrange interpolation and B-spline basis functions, was used for approximation.
  • The correction function was applied to non-bandlimited waveforms to suppress aliasing.

Main Results:

  • The ideal bandlimited step function was shown to be equivalent to the sine integral.
  • Integrated polynomial interpolation effectively approximated the bandlimited step function.
  • The proposed technique demonstrated a superior tradeoff between computational cost and sound quality compared to existing methods.

Conclusions:

  • The integrated third-order B-spline correction function provides perceptually aliasing-free sawtooth emulation.
  • This method achieves aliasing-free sound up to 7.8 kHz at a 44.1 kHz sample rate.
  • The technique offers an efficient solution for high-fidelity digital music synthesis.