Apparatus and method for approximating an exponential decay in a sound synthesizer

A linear approximation to an exponential decay function exploits the characteristic of an exponential function that, at equal time intervals, the ratio of a parameter value at the beginning of the interval to the parameter value at the end of the interval remains constant. The technique for linear approximation of an exponential decay includes selection of a constant period or interval of time and selection of a constant ratio between the parameter value at the beginning of the constant period and the parameter value at the end of the constant period. In one embodiment, the selected ratio is one-half to exploit a binary arithmetic implementation. For a ratio of one-half, the exponential decay has a ""half-life"" in which only half the parameter value at the beginning of a period is left at the end of the selected ""half-life time period"".