METHOD FOR DISCRETE TRANSFORMATION OF SIGNALS BASED ON ORTHOGONAL POLYNOMIALS

摘要

FIELD: physics.;SUBSTANCE: signal readings are broken into units having N₁ items, unit from N₁ to N readings is non-uniformly cut in accordance with the law of the order of zeroes of the orthogonal polynomial, zero or first order interpolation is carried out to obtain N samples or a signal section is non-uniformly sampled in accordance with a law determining the order of zeroes of the orthogonal polynomial to obtain N samples, forward polynomial transformation by multiplying N samples by transformation matrix with elements p_m(x_i), m=0…(M-1) from readings of orthogonal polynomials and multiplying by weight coefficients λ_i, determined by the type of orthogonal polynomial, is carried out to obtain M spectral coefficients, inverse polynomial transformation of M spectral coefficients to L signal readings is carried out.;EFFECT: faster calculation of the component of the generalised signal spectrum, reduced distortions of the reconstructed signal caused by errors in transforming the signal into spectra and spectrum into signal, high signal compression coefficient owing to further cutting of readings in accordance with the law of the order of zeroes of the orthogonal polynomial, possibility of scaling and shifting the reconstructed signal without further interpolation operations.;4 cl, 4 dwg