Refining oscillatory signals by non-stationary subdivision schemes

The paper presents a method for refining real highly oscillatory signals. The method is based upon interpolation by a finite set of trigonometric basis functions. The set of trigonometric functions is chosen (identified) by minimizing a natural error norm in the Fourier domain. Both the identification and the refining processes are computed by linear operations. Unlike the Yule-Walker approach, and related algorithms, the identification of the approximating trigonometric space is not repeated for every new input signal. It is rather computed off-line for a family of signals with the same support of their Fourier transform, while the refinement calculations are done in real-time. Statistical estimates of the point-wise errors are derived, and numerical examples are presented.