  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 {\psi},of the time
variable t, a set of functions {\Psi}_n which depend on time, frequency and
frequency (or time) standard deviation. Some properties of the transformations
T_n and the functions {\Psi}_n are given. It is proved in particular that the
square of the modulus of each function {\Psi}_n can be interpreted as a
representation of the energy distribution of the signal, represented by the
function {\psi}, in the time-frequency plane for a given value of the frequency
(or time) standard deviation. It is also shown that the function {\psi}, can be
recovered from the functions{\Psi}_n.
