Using the invariant imbedding method, we study numerically the statistical characteristics of backscattering of plane-wave pulses incident normally on a random one-dimensional medium. The local reflection coefficient of the medium is simulated by a centered Gaussian process with an exponential correlation function. We consider the time dependences of the average intensity and the kurtosis coefficient of reflections for various durations and carrier frequencies of the initial signal. It is shown that the attenuation and fluctuations of reflections increase with the initial-signal duration normalized to the time scale of the medium irregularities and depend on the signal carrier. Numerical results for the average intensity are compared with previously obtained analytical solutions. We discuss the appearance conditions of a wave stochastic resonance in nonstationary reflections.
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