On analysis of exponentially decaying pulse signals using stochastic volatility model

Abstract

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.

On analysis of exponentially decaying pulse signals using stochastic volatility model. Part II: Student-t distribution

“…The present u is basically the same as those obtained using the EP distribution with a kurtosis of 0.75. 3 The variation pattern of h is also very close to that shown in Chan et al 3 Further increas- ing ␣ may result in a slightly better performance, but the very computer resources demanding calculation makes it impractical.…”

“…However, the pulse initiation and its eventual decay are still observable with the EP distribution at this signal-to-noise ratio level. 3 Results for ␣ Ͻ 30 are not presented as they are all worse than those shown in Figs. 1 and 2.…”

“…Table II summarizes the performance of the present SV model and has it compared with that of the previous study of the authors. 3 One can find that the use of the EP distribution in the SV model results in a better analysis when the S/N drops below 3 dB. The somewhat worse performance of the Student-t distribution overall may be due to the relatively longer tail of the Student-t distribution compared to those of the EP family with small kurtosis even when the degree of freedom is large.…”

“…The artificial signals in Chan et al 3 are adopted again in the present study. They consist of an exponentially decaying harmonic wave s and Gaussian white noises of various levels…”

“…The recent study of the authors 3 illustrates that the stochastic volatility ͑SV͒ model incorporating the exponential power distribution ͑EP͒ is able to retrieve the instant of the pulse initiation and the decay constant within engineering tolerance even when the background noise level is comparable to that of the pulse. Its performance is much better than that of the conventional short-time Fourier transform when there is a small fluctuation in the frequency of the decaying pulse.…”