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We analyze the records of Jupiter’s decameter radio emissions obtained during an Io-A S-burst storm on 15 March 2005. The observations were performed at the world’s largest decameter array, UTR-2, which is equipped with a digital receiver capable of catching waveforms of duration _3 s with temporal resolution defined by the sampling rate of _66 MHz. A Hilbert transform based algorithm has been applied to study narrowband spectral patterns demonstrating quasi-linear drift over time-frequency plane. The instantaneous amplitude and phase information has been extracted from the recorded waveforms with the purpose of analyzing microsecond-scale coherent events in the S-burst emission. A statistical model of narrow band random process is proposed for describing such features in the observed waveforms as coherent segments, phase jumps, nonlinear frequency drift, etc. It is shown that the study of coherence properties in terms of instantaneous phase is equivalent to Fourier analysis of a narrowband signal. This implies that no particular mechanism (such as superimposed modulation or oscillation) is required for generating the observed coherent phase structures of S-burst emission: those, as well as the pulse-like envelope structures, emerge naturally at the output of a narrow band filter applied to a random noise. It is further suggested that probability distribution function of instantaneous amplitude gives an important insight into the underlying physical mechanism of S-burst generation. In particular, it is demonstrated that models based on the concept of ‘‘generator,’’ i.e., a nonlinear system with feedback, are less suitable for reproducing the observational characteristics of S-bursts at microsecond time scale resolution. On the other hand, the concept of ‘‘amplifier,’’ i.e., a linear system (without feedback) that enhances the fluctuations within a narrow band, fits the observational data well. This conclusion is consistent with S-burst generation mechanism via cyclotron-maser instability, which is indeed a resonant wave amplification process