Title :
Closed-form correlation functions of generalized Hermite wavelets
Author :
De Abreu, Giuseppe Thadeu Freitas
Author_Institution :
Center for Wireless Commun., Univ. of Oulu, Finland
fDate :
6/1/2005 12:00:00 AM
Abstract :
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.
Keywords :
Gaussian processes; correlation methods; polynomials; signal processing; wavelet transforms; Hermite polynomial; closed-form correlation function; generalized Hermite wavelet; impulsive waveform; signal processing; Biomedical signal processing; Continuous wavelet transforms; Gaussian processes; Image coding; Mathematics; Polynomials; Radar signal processing; Signal processing; Wavelet analysis; Wavelet transforms; Correlation functions; Hermite expansions; Hermite wavelets;
Journal_Title :
Signal Processing, IEEE Transactions on
DOI :
10.1109/TSP.2005.847855
