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