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A Method for Envelope Warping in Digital Audio Synthesis

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The use of stored envelope functions is common to many audio signal synthesis techniques. This table lookup method is susceptible to audible defects in the synthesized output if care is not taken in the design of the synthesis algorithm, particularly when the rate at which values from the envelope table are accessed is to vary with time. A useful strategy is presented for altering the effective lookup rate for a stored envelope function in order to minimize audible discontinuities between envelope segments with differing lookup rates. The approach creates a smooth warping of the stored envelope function by forcing the envelope lookup index (the envelope phase) to vary according to a cubic polynomial function with matched transitions from envelope segment to segment.

JAES Volume 39 Issue 12 pp. 934-944; December 1991
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AES - Audio Engineering Society