V.G. Guetmanov, S.E. Orlov

The article describes filtration method of the noise affected sound signals by using approximation splines. The question of aproximation splines filtration was raised in general terms. The mathematical design to set up aproximation splines by using the discrete orthogonal polynoms calculated through recurrent equations is offered. The mathematical design outcome is system of linear equations which result with allocation of approximation spline function. Description for spline approximation filter was obtained. The case of spline approximation application for long length sound signals filtration was addressed separately. The application method for spline approximation filtration at spline intervals with fixed set of points is offered and guarantees flatness of spline function in junction points. The efficiency of spline approximation filter for the noise affected sound signals was analyzed in comparison with traditional digital low-pass Butterworth filter. Both filters performance for initial signal was compared under clear sound and affected sound conditions. The comparison result allowed to justify some advantages of spline approximation filter over traditional one. For clear sound signal Butterworth filter provided the presence of phase shifts caused by filtration process whereas it was not recognized with approximation spline filter. For sound signal affected by white noise the error values of performance for both filters were obtained with the help of statistical modelling. The statistical modelling carried out showed higher efficiency of spline approximation filter in comparison with traditional one. The quality of both signals gained during filtration was evaluated by an expert group. During the experiment three signals were reproduced consequently as initial sound signal 1, sound signal 2 filtered with Butterworth filter and sound signal 3 filtered with spline approximation filter. In accordance with expert's opinion the quality of sound signal 3 is higher than sound signal 2 and approaching the quality of initial sound signal.