Efficient antialiasing oscillator algorithms using low-order fractional delay filters

  • Authors:

  • Juhan Nam;Vesa Välimäki;Jonathan S. Abel;Julius O. Smith

  • Affiliations:

  • Center for Computer Research in Music and Acoustics, Stanford University, Stanford, CA;Department of Signal Processing and Acoustics, TKK, Helsinki University of Technology, Espoo, Finland and Center for Computer Research in Music and Acoustics, Stanford University, Stanford, CA;Center for Computer Research in Music and Acoustics, Stanford University, Stanford, CA;Center for Computer Research in Music and Acoustics, Stanford University, Stanford, CA

  • Venue:
  • IEEE Transactions on Audio, Speech, and Language Processing - Special issue on virtual analog audio Effects and musical instruments
  • Year:
  • 2010

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Abstract

One of the challenges in virtual analog synthesis is avoiding aliasing when generating classic waveforms such as sawtooth and square wave which have theoretically infinite bandwidth in their ideal forms. The human auditory system renders a certain amount of aliasing inaudible, which allows room for finding cost-effective algorithms. This paper suggests efficient algorithms to reduce the aliasing using low-order fractional delay filters in the framework of bandlimited impulse train (BLIT) synthesis. Examining Lagrange, B-spline interpolators and allpass fractional delay filters, optimized methods will be discussed for generating classic waveforms (sawtooth, square, and triangle). Techniques for generating more complicated harmonics such as pulse width modulation, hard-sync, and super-saw are also presented. The perceptual evaluation is performed by comparing the threshold of hearing and masking curve of oscillators with their aliasing levels. The result shows that the BLIT using the computationally efficient thirdorder B-spline generates waveforms that are perceptually free of aliasing within practically used fundamental frequencies.