1. A method for data padding and noise filtering implemented on a digital processing device, comprising the steps of: a. defining a total data set as the collection of all known and unknown data, where the unknown values may be interspersed among the known values, or concentrated in a region adjacent to the known values, or a combination of the two; b. placing the unknown values of the data to be obtained by a padding procedure so that the total data set contains only equally space data—the data has a constant sampling interval and the total data set represents a function; c. calculating an appropriate difference between the true data and an approximation to the data for all known and unknown data values; d. minimizing the difference with respect to the unknown data values by iteration or using the calculus of variations to obtain algebraic equations for the unknown values or solving the algebraic equation for the unknown data values.