GENERAL DIAGNOSTIC AND REAL-TIME APPLICATIONS OF DISCRETE HERMITE FUNCTIONS TO DIGITAL DATA

General diagnostic and real-time application of digital Hermite functions allows features to be extracted from a measured signal through expansion of the measured signal. Specifically, the digital Hermite functions represent the shape of the measured signal in a set of vectors derived from a symmetrical tridiagonal matrix. This allows for efficient computation of the Hermite expansion coefficients, in real-time, to represent the expanded signal. The signal expansion also allows any artifacts, such as noise, to be isolated and removed, allowing the underlying signal of interest to be revealed.