pulsemodel

Pulsemodel is a mathematical framework used to describe short-duration transient signals, or pulses, in time-domain data. It provides a compact, parameterized representation that captures a pulse’s amplitude, timing, and shape, enabling analysis, synthesis, and interpretation of pulsed phenomena across disciplines. A pulsemodel can be built from simple shapes such as rectangular, Gaussian, exponential, or double-exponential forms, or from more flexible families like generalized Gaussian or gamma distributions. In practice, a pulse is described by parameters including peak amplitude, start time, duration or width, and sometimes rise and fall times or asymmetry.

Parameter estimation involves fitting the chosen pulse form to data, typically by least-squares optimization, maximum likelihood, or Bayesian methods. Achieving robust fits requires accounting for noise, background level, and potential overlap when multiple pulses occur in rapid succession. Pulse characteristics are summarized with metrics such as full width at half maximum, rise time, fall time, and symmetry.

Pulsemodels are used across fields where brief signals occur. In electronics and communications, they model transmitted or received pulses; in optics and ultrafast science, they describe laser pulses; in neuroscience and physiology, they approximate action potentials or hemodynamic responses; in spectroscopy and lidar, they characterize instrument response and reflected signals.

Limitations include model mismatch to actual signals and sensitivity to noise. Selecting an appropriate pulseform, validating the fit against independent data, and assessing uncertainty are essential steps in reliable pulse modeling.