Application of the Hermite basis for spectral analysis

The work is concerned with an application of the Hermite functions in signal approximation. The purpose of the work is to show their properties in time and frequency domains, namely their orthogonality, Fourier transform, zeros and asymptotic behaviour as their order becomes high. The next subject of this work is the question of scaling these functions to minimize the square error of signal approximation. Several methods proposed by different authors are discussed. Finally these algorithms are tested by approximating simple signals so that their results can be compared