Meaning of formulation of generalized inverse Kotelnikov’s theorem

On the basis of known mathematical facts a formulation of generalized inverse Kotelnikov’s theorem is considered for continuous signals presented by a Fourier series in non-trigonometric ortogonal systems. An algorithm is proposed basing on the mentioned theorem as that of existence, for transforming the equally spaced readings into the non-equally spaced ones with approximation of intermediate signals by splines and appropriate choice of approximation nodes.