Year: 2013
Type: article
Abstract: A method for time-frequency analysis is given. The approach utilizes properties of Gaussian distribution, properties of Hermite polynomials and Fourier analysis. We begin by the definitions of a set of functions called Harmonic Gaussian Functions. Then these functions are used to define a set of transformations, noted T_n, which associate to a function ψ, of the time variable t, a set of functions Ψ_n which depend on time, frequency and frequency (or time) standard deviation. Some properties of the transformations T_n and the functions Ψ_n are given. It is proved in particular that the square of the modulus of each function Ψ_n can be interpreted as a representation of the energy distribution of the signal, represented by the function ψ, in the time-frequency plane for a given value of the frequency (or time) standard deviation. It is also shown that the function ψ can be recovered from the functions Ψ_n.
Author: Tokiniaina Ranaivoson
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2131636581