Optimal interval of linear interpolation

Abstract

There is no optimal (in the sense of mean square error) interval of Tₒₚₜ interpolation by one, two, three, etc. equal to T ordinates of the “pure” signal x (t). The smaller T, the smaller the mean square of the error. If an interference n (t) is added to the signal, then for one-point (step) interpolation Tₒₚₜ also does not exist at any combinations of x (t) and n (t). However, already for two-point (linear) interpolation, the interval Tₒₚₜ, which gives the minimum of RMS error, exists, and linear interpolation of discrete measurements can be more accurate than continuous measurements. At the same time, linear preemptive extrapolation does not improve the accuracy.

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