About a Partial Differential Equation-Based Interpolator for Signal Envelope Computing: Existence Results and Applications

Abstract

This paper models and solves the mathematical problem of interpolating characteristic points of signals by a partial differential Equation-(PDE-) based approach. The existence and uniqueness results are established in an appropriate space whose regularity is similar to cubic spline one. We show how this space is suitable for the empirical mode decomposition (EMD) sifting process. Numerical schemes and computing applications are also presented for signal envelopes calculation. The test results show the usefulness of the new PDE interpolator in some pathological cases like input class functions that are not so regular as in the cubic splines case. Some image filtering tests strengthen the demonstration of PDE interpolator performance.