Piecewise-linear approximation of additive synthesis envelopes: A comparison of various methods

Piecewise-linear approximation of additive-synthesis amplitude and frequency envelopes is one of the most common data-reduction techniques used in sound synthesis. This paper examines and compares a number of methods for determining a prescribed number of breakpoint times in order to achieve the best line-segment approximations to the amplitude envelopes of a sound's harmonics. The method uses a set of breakpoint times that are common to all harmonics, and it samples amplitudes values from the original envelopes at the selected times. Resynthesis uses additive synthesis or, more efficiently, linear interpolation between waveforms that represent the spectrum at each breakpoint