Efficient Antialiasing Oscillator Algorithms Using Low-Order Fractional Delay Filters

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 third-order B-spline generates waveforms that are perceptually free of aliasing within practically used fundamental frequencies.

[1]  J. Moorer.  The Synthesis of Complex Audio Spectra by Means of Discrete Summation Formulas , 1976 .

[2]  Eli Brandt,et al.  Hard Sync Without Aliasing , 2001, ICMC.

[3]  Robert Bristow-Johnson,et al.  Performance of Low-Order Polynomial Interpolators in the Presence of Oversampled Input , 1999 .

[4]  Hal Chamberlin.  Musical Applications of Microprocessors , 1980 .

[5]  Ernst Terhardt,et al.  Calculating virtual pitch , 1979, Hearing Research.

[6]  Andreas Franck,et al.  Efficient Algorithms and Structures for Fractional Delay Filtering Based on Lagrange Interpolation , 2009 .

[7]  Vesa Välimäki,et al.  Energy-based effective length of the impulse response of a recursive filter , 1998, Proceedings of the 1998 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '98 (Cat. No.98CH36181).

[8]  Karlheinz Brandenburg,et al.  A Closed-Form Description for the Continuous Frequency Response of Lagrange Interpolators , 2009, IEEE Signal Processing Letters.

[9]  Richard G. Lyons.  DC Blocker Algorithms , 2012 .

[10]  E. Hermanowicz,et al.  Explicit formulas for weighting coefficients of maximally flat tunable FIR delayers , 1992 .

[11]  Vesa Välimäki,et al.  Filter-based alias reduction for digital classical waveform synthesis , 2008, 2008 IEEE International Conference on Acoustics, Speech and Signal Processing.

[12]  Vesa V Alim Aki.  Discrete-Time Modeling of Acoustic Tubes Using Fractional Delay Filters , 1995 .

[13]  Michael Unser,et al.  Splines: a perfect fit for signal and image processing , 1999, IEEE Signal Process. Mag..

[14]  Vesa Välimäki,et al.  Oscillator and Filter Algorithms for Virtual Analog Synthesis , 2006, Computer Music Journal.

[15]  Kenneth Steiglitz,et al.  Input Generators for Digital Sound Synthesis , 1970 .

[16]  Vesa Välimäki.  Discrete-time synthesis of the sawtooth waveform with reduced aliasing , 2005, IEEE Signal Processing Letters.

[17]  R. Lyons,et al.  DC Blocker Algorithms[DSP Tips & Tricks] , 2008, IEEE Signal Processing Magazine.

[18]  Mathieu Lagrange,et al.  Real-Time Additive Synthesis of Sound by Taking Advantage of Psychoacoustics , 2001 .

[19]  Vesa Välimäki,et al.  Antialiasing Oscillators in Subtractive Synthesis , 2007, IEEE Signal Processing Magazine.

[20]  Vesa Vlimki,et al.  Discrete-Time Modeling of Acoustic Tubes Using Fractional Delay Filters , 1998 .

[21]  Unto K. Laine,et al.  Splitting the unit delay [FIR/all pass filters design] , 1996, IEEE Signal Process. Mag..

[22]  Julius O. Smith,et al.  Alias-Free Digital Synthesis of Classic Analog Waveforms , 1996, ICMC.

[23]  John E. Lane,et al.  Modeling analog synthesis with DSPs , 1997 .

[24]  Dana C. Massie.  Wavetable Sampling Synthesis , 2002 .

[25]  Marina Bosi,et al.  AUDIO CODING: BASIC PRINCIPLES AND RECENT DEVELOPMENTS , 2003 .

[26]  Julius O. Smith,et al.  Efficiently-variable non-oversampled algorithms in virtual-analog music synthesis: a root-locus perspective , 2006 .

[27]  Peter J. Kootsookos,et al.  FIR approximation of fractional sample delay systems , 1996 .

[28]  I. J. Schoenberg.  Contributions to the problem of approximation of equidistant data by analytic functions. Part A. On the problem of smoothing or graduation. A first class of analytic approximation formulae , 1946 .

[29]  Max V. Mathews,et al.  The Technology Of Computer Music , 1970 .

[30]  Joseph Timoney,et al.  A modified FM synthesis approach to bandlimited signal generation , 2008 .

[31]  Vesa Välimäki,et al.  A computationally efficient coefficient update technique for Lagrange fractional delay filters , 2008, 2008 IEEE International Conference on Acoustics, Speech and Signal Processing.