HERMITE SIEVE AS A WAVELET-LIKE ARRAY FOR 1D AND 2D SIGNAL DECOMPOSITION

A new class of an array of wavelet-like functions, derived from genera lised Hermite polynomials and controlled by a scale parameter, has bee n used to create a multilayered representation for one- and two-dimens ional signals. This representation, which is explicitly in terms of an array of coefficients, reminiscent of Fourier series, is stable. Amon g its other properties, (a) the shape of the resolution cell in the 'p hase-space' is variable even at a specified scale, depending on the na ture of the signal under consideration; and (b) zero crossings at the various scales can be extracted directly from the coefficients. The ne w representation is illustrated by examples. However, there do remain some basic problems with respect to the new representation.