GENERALIZED HARMONIC-ANALYSIS AND EPSILON -DISTRIBUTION

The energy spectral distribution of a signal, with finite integrated s quare modulus (energy), is given by classical harmonic analysis, the p ower spectral distribution of a signal, with finite square modulus mea n value (power), is given by Wiener's generalized harmonic analysis. T he power spectral distribution is linked to what can be called integra l Fourier transform of this signal which has interesting properties. O ne of them, of difficult access, can be established directly with the help of the proposed formalism of the ''epsilon distribution'', which seems adapted to generalized harmonic analysis. The ''epsilon distribu tion'' can be described, heuristically, as a pseudo-function equal to zero on [ - infinity, + infinity] with an integral nevertheless equal to one and, along the lines of distributions theory, as a linear opera tor which, acting upon an acceptable function, gives ifs mean value on [- infinity, + infinity].