In an apparatus for generating an aperiodic waveform having a gradually decaying envelope, a sequence of digital samples representing the magnitude of the waveform at sample points is stored in a memory. The stored digital samples are grouped into at least first and second continuous portions, the second portion including that portion of the sequence in which none of the digital samples has a magnitude exceeding 1/n the magnitude of the largest of the digital samples, where n is an integer greater than unity, each of the digital samples of the second portion being scaled by a factor of n. The memory further stores a code indicating the beginning of the second portion. An address counter develops an address signal for sequentially addressing the stored digital samples and code from the memory in response to clock pulses. When the stored code is addressed, an additional clock pulse is supplied from a code detector to the address counter. Each of the addressed digital samples of the first and second portions is scaled and converted to a signal having a magnitude corresponding to the magnitude of the associated digital sample of the sequence.