A stochastic volatility model incorporated the exponential power distributions and Student – t distributions are adopted in this book to analyze exponentially decay pulses in the presence of background noises of various magnitudes. It is found that the present stochastic volatility model can retrieve the instant of the pulse initiation and the decay constant within engineering tolerance even when the noise is slightly stronger that the pulse amplitude. The results suggest that both these distributions can give accurate recovery of the instants when the abrupt changes take place if the background noise level is lower than that of the changes by 3dB. The results are compared with those obtained by the conventional short-time Fourier transform and its performance is considerably better than that of the latter when the frequency of the decay pulse fluctuates. To recover the initialization of an exponentially growing wave embedded inside a stationary background noise is...