On analysis of exponentially decaying pulse signals using stochastic volatility model

A stochastic volatility model incorporating the exponential power distributions is adopted in the present study to analyze exponentially decaying pulses in the presence of background noises of various magnitudes. The discussions are focused on its effectiveness in the determination of the instant of the pulse initiation and the decay constant. The results are compared with those obtained by the conventional short-time Fourier transform. 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. Its performance is substantially better than that of the Fourier transform when the frequency of the decay pulse fluctuates.