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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]

We consider the reconstruction of signals from nonuniformly spaced samples using a projection onto convex sets (POCSs) implemented with the evolutionary time-frequency transform. Signals of practical interest have finite time support and are nearly band-limited, and as such can be better represented by Slepian functions than by sinc functions. The evolutionary spectral theory provides a time-frequency representation of nonstationary signals, and for deterministic signals the kernel of the evolutionary representation can be derived from a Slepian projection of the signal. The representation of low pass and band pass signals is thus efficiently done by means of the Slepian functions. Assuming the given nonuniformly spaced samples are from a signal satisfying the finite time support and the essential band-limitedness conditions with a known center frequency, imposing time and frequency limitations in the evolutionary transformation permit us to reconstruct the signal iteratively. Restricting the signal to a known finite time and frequency support, a closed convex set, the projection generated by the time-frequency transformation converges into a close approximation to the original signal. Simulation results illustrate the evolutionary Slepian-based transform in the representation and reconstruction of signals from irregularly-spaced and contiguous lost samples.

Recently, information technology and microelectronics have enabled implanting miniature and highly intelligent devices within the brain for in-vitro diagnostic and therapeutic functions. Power and physical size constraints of these devices necessitate novel signal processing methods. In this paper we investigate an effective data acquisition and reconstruction method for brain implants based on Asynchronous Sigma Delta Modulators (ASDMs). The ASDMs are analog non-linear feedback systems capable of time coding signals. The proposed reconstruction algorithm is based on the Prolate Spheroidal Wave Function (PSWF) expansion of the sinc functions and the order of expansion is given by the input signal being coded. Multiplexing and transmission of the different channels of data are accomplished by chirp orthogonal frequency division multiplexing. Computer simulations using multi channel electroencephalographic data are performed for wireless transmission by brain implants for monitoring abnormal brain activities of epilepsy patients.