Refining Oscillatory Signals by Non—Stationary Subdivision Schemes

Abstract

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.