Closed-form correlation functions of generalized Hermite wavelets

A closed-form expression is given for the correlation functions of generalized Hermite wavelets, constructed from an also-generalized definition of Hermite polynomials. Due to their Gaussianity, these wavelets can be used as a tool in the analysis or design of systems involving nonsinusoidal wavelets as well as to model impulsive waveforms found in real-world applications and signal processing problems. As such, the formula is potentially applicable to various areas of science.

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