An Error Analysis for the Sampling of Periodic Signals
Mathews Jacob, Thierry Blu, Michael A. Unser · Infoscience (Ecole Polytechnique Fédérale de Lausanne) · 2001
Abstract|We analyze the representation of peri-odic signals in a scaling function basis. This rep-resentation is suÆciently general to include the widely used approximation schemes like wavelets, splines and Fourier series representation. We de-rive a closed form expression for the approximation error in the scaling function representation. The error formula takes the simple form of a Parseval like sum, weighted by an appropriate error kernel. This formula may be useful in choosing the right representation for a class of signals. We also exper-imentally verify the theory in the particular case of description of closed curves. I.