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Multi‐resolution analysis methods can reveal the underlying physical dynamics of nonstationary signals, such as those from lightning. In this paper we demonstrate the application of two multi‐resolution analysis methods: Ensemble Empirical Mode Decomposition (EEMD) and Variational Mode Decomposition (VMD) in a comparative way in the analysis of electric field change waveforms from lightning. EEMD and VMD decompose signals into a set of Intrinsic Mode Functions (IMFs). The IMFs can be combined using distance and divergence metrics to obtain noise reduction or to obtain new waveforms that isolate the physical processes of interest while removing irrelevant components of the original signal. We apply the EEMD and VMD methods to the observations of three close Narrow Bipolar Events (NBEs) that were reported by Rison et al. (2016, https://doi.org/10.1038/ncomms10721). The ΔE observations reveal the occurrence of complex oscillatory processes after the main NBE sferic. We show that both EEMD and VMD are able to isolate the oscillations from the main NBE, with VMD being more effective of the two methods since it requires the least user supervision. The oscillations are found to begin at the end of the NBEs' downward fast positive breakdown, and appear to be produced by a half‐wavelength standing wave within a weakly‐conducting resonant ionization cavity left behind in the wake of the streamer‐based NBE event. Additional analysis shows that one of the NBEs was likely initiated by an energetic cosmic ray shower, and also corrects a misinterpretation in the literature that fast breakdown is an artifact of NBE‐like events in interferometer observations. Plain Language Summary: This paper investigates the application of mode decomposition techniques to the analysis of Narrow Bipolar Events (NBEs). NBEs are high‐power discharges that often occur as the initiating event of lightning flashes, and are produced by streamer‐based activity called fast positive breakdown. We apply Ensemble Empirical Mode Decomposition (EEMD) and Variational Mode Decomposition (VMD) methods to three NBEs that were observed at Langmuir Laboratory in New Mexico to extract and interpret oscillatory behavior that occurred following the NBEs. We show that both EEMD and VMD separate the oscillations from the strong electric field change of the parent NBE, with VMD being the preferred choice. The resulting waveforms are indicative of a shock‐excited residual process that lasts for tens of microseconds, beginning at the end of the downward fast breakdown activity. Although questions remain about the physical mechanism of the oscillations, they appear to be caused by the NBE's streamers creating a weakly‐conducting resonant cavity in its wake that supports half‐wavelength standing wave oscillations, analogous to the vibrations of a plucked guitar string. Key Points: Ensemble Empirical Mode Decomposition and Variational Mode Decomposition separate out Narrow Bipolar Event (NBE) oscillations for further studies of physical mechanisms responsible for oscillationsThe results show the oscillations initiate not during the NBE but at the end of the fast positive breakdown processThe oscillatory behavior indicates that residual ionic conductivity creates a resonant cavity which emits half‐wavelength radiation [ABSTRACT FROM AUTHOR]

Based on the ensemble empirical mode decomposition (EEMD) method, a DAF method for signal construction is proposed that repeatedly decomposes (D) the signal, amplifies (A) the local signal characteristics, and then filters (F) the signal. This method is used to decompose and reconstruct the electric field waveform (called a sferic) of an energetic in-cloud pulse (EIP) with a 247-kA peak current detected by a fast antenna (FA). Based on synchronous sub-microsecond very high-frequency (VHF, 14–88 MHz) radio interferometer (INTF) observations and observed downward fast positive and upward fast negative breakdowns, which occurred simultaneously with the EIP, the EIP sferic is decomposed by the DAF method in 11 steps into two independent sferics: a smoother filtered EIP sferic and an embedded narrow bipolar-like event (NBE). It is verified that strong VHF radiation is generated by the NBE-like event, rather than being associated with the smooth EIP sferic. The analysis, decomposition, and reconstruction of the correlated signals by the EEMD-based DAF method proposed in this article support the idea that the large-amplitude EIP sferic was generated by relativistic discharge responsible for an accompanying terrestrial gamma-ray flash (TGF) rather than by streamer or leader activity. [ABSTRACT FROM AUTHOR]