Economical generation of exponential and pseudo-exponential decay

Abstract

Exponential and pseudo-exponential decay function values are generated by scaling a fractional decrease per sampling period by a previous decay function value and then subtracting the scaled fractional decrease from the previous decay function value. In one embodiment, a multiplier multiplies the fractional decrease by the previous decay function value and provides a product signal representing the scaled fractional decrease. An adder subtracts the scaled fractional decrease from the previous decay function value. In another embodiment, a shift block replaces the multiplier and approximates multiplication by a binary shift of the fractional decrease. The size of the shift is determined by the previous magnitude of the decay function as indicated by a priority encoder. Shifting generates a pseudo-exponential decay function which is suitable for music synthesis and can be generated quickly using less expensive hardware.