Gunfire is used as an example to illustrate how the Karhunen-Loeve (K-L) expansion can be used to characterize and simulate nonstationary random events. This paper will develop a method to describe the nonstationary random process in terms of a K-L expansion. The gunfire record is broken up into a sequence of transient waveforms, each representing the response to the firing of a single round. First, the mean is estimated and subtracted from each waveform. The mean is an estimate of the deterministic part of the gunfire. The autocovariance matrix is estimated from the matrix of these single-round gunfire records. Each column is a realization of the firing of a single round. The gunfire is characterized with the K-L expansion of the autocovariance matrix. The gunfire is simulated by generating realizations of records of a single-round firing from the expansion and the mean waveform. The individual realizations are then assembled into a realization of a time history of many rounds firing. The method is straightforward and easy to implement, and produces a simulated record very much like the original measured gunfire record.

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