Subsample Precise Granular Synthesis

Granular Synthesis

The term Granular Synthesis refers to synthesis techniques based on assembling new sounds from short waveform particles. The waveform particles referred to as grains are typically between 10 to 50 ms long and possibly overlap. Early examples are Iannis Xenakis' Analogique A-B which the composer created by splicing magnetic tape. Various analog devices which essentially implement granular synthesis were developed including Gabor's optical system based on a film projector, the Springer Tempophon, and the phonogene which are magnetic tape machines with multiple rotating tape heads. Digital implementations were made popular by Curtis Roads and Barry Truax. By means of computer programming many varieties of granular synthesis with different control parameters are implemented since then. A potential problem with digital implementations is the quantization of the onset times due to the sampling rate. Especially for periodically repeated grains aliasing components are introduced to the output sound, caused by timing jitter in the durations between the grain onsets. This can be avoided by subsample precise grain placement.

Avoiding Onset Time Jitter

Since discrete time implementations do not allow grains to start at time points falling in between the sampling instances, timing jitter can lead to audible artifacts if the onset times are quantized (rounded to the closest sampling instance). The effect of timing jitter on an impulse train is analyzed by Tim Stilson in [stils1]. The aliased impulse train can be interpreted as a sequence of regular sampled rectangular pulses of one sample width. To generate an aliasing free pulse-train, the rectangular (non band-limited pulses) can be replaced by windowed sinc functions. By sampling windowed sinc functions, discrete signals representing impulses at arbitrary time instances can be produced. Convolving such a signal (containing arbitrarily spaced band-limited impulses) with a grain yields a signal containing fractionally delayed grains. Therefor subsample precise granular synthesis can be implemented by convolving sampled band-limited impulses with the grain waveform. The drawback is a loss of generality. The grains itself cannot be parametrized except for their amplitude. In traditional granular synthesis, grains are usually modified by individual amplitude envelopes and/or variable playback speed. This parameters are often controlled by stochastic processes. Instead of convolving the fractionally sampled impulses with the grain, the grain can be fractionally delayed by a filter following the grain playback function. This way not only generality is preserved but due to the usually sparse nature of the onset times (an impulse signal representing the triggers containing mostly zero samples) it is also less CPU intensive.

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Bran, Germ, Endosperm

A tape piece exploring structures on time scales where rhythm perception and pitch perception overlap. The piece makes extensive use of the technique described in this document. The granular synthesis output is fed into an LPC Vocoder. Towards the end of the piece more and more clear vocal like spectral modifications occur until it clearly turns into the voice of a frenchman who appears to speak with a complaining intonation. Partly the speech is not clearly articulated, but sometimes understandable phrases like ``...I would be more interested in a university paper...'', appear in the voice-like organic stream of sounds.

Listen to Bran, Germ, Endosperm

Bibliography

1
D. Gabor.
Acoustical quanta and the theory of hearing.
Nature, 159(4044):591-594, 1947.

2
C. Roads.
Introduction to granular synthesis.
Computer Music Journal, 12(2):11-13, 1988.

2
T. Stilson.
Alias-Free Digital Synthesis of Classic Analog Waveforms.
1996.

3
C. Roads.
Microsound.
Cambridge, MA: The MIT Press, 2001.

4
B. Truax.
Real-time granular synthesis with a digital signal processor.
Computer Music Journal, 12(2):14-26, 1988.

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Copyright © 1993, 1994, 1995, 1996, Nikos Drakos, Computer Based Learning Unit, University of Leeds.
Copyright © 1997, 1998, 1999, Ross Moore, Mathematics Department, Macquarie University, Sydney.

Bjoern Erlach 2010-06-24