Generation of Dirac Pulses from Voltage Threshold Crossing Times in the Time Domain for Fundamental Frequency, Phase Difference, and Noise Parameter Estimation

Abstract This paper proposes a novel event-based statistical framework for analog signal analysis and transmission in the time domain. Unlike conventional signal processing methods based on uniform sampling and frequency-domain analysis, the proposed framework represents the signal through multi-level voltage threshold crossings. The signal amplitude is partitioned into discrete voltage levels between its minimum and maximum values. Each threshold crossing generates a Dirac impulse, producing a sparse temporal event representation of the original waveform. The generated event sequence is analyzed statistically by computing the distributions of repeated time intervals between consecutive events. These statistical features are used to estimate the fundamental frequency, phase information, and deterministic interference components. The framework further proposes a frequency relationship in which deterministic interference frequencies are expressed as integer multiples of the fundamental frequency multiplied by an experimentally estimated correction factor. This relationship provides a compact representation for identifying both the useful signal and interference components. Instead of transmitting a large number of uniformly sampled amplitudes, the proposed method transmits a compact set of statistical parameters describing the signal. At the receiver, these parameters are used together with the reconstruction algorithm to regenerate the original signal while simultaneously identifying and reducing deterministic interference. The proposed framework therefore aims to reduce transmitted data, computational complexity, and bandwidth requirements while preserving the essential information required for signal reconstruction. The proposed methodology integrates voltage-level decomposition, Dirac event generation, statistical interval analysis, and model-based reconstruction into a unified time-domain signal processing framework. Its theoretical properties and practical performance will be evaluated through mathematical analysis, numerical simulations, and comparisons with conventional techniques such as Shannon sampling, FFT, Welch spectral estimation, and wavelet-based methods. Keywords: Event-based signal processing, Time-domain analysis, Voltage threshold crossings, Dirac impulses, Statistical interval analysis, Frequency estimation, Signal reconstruction, Deterministic interference, Signal transmission.