Method of Harmonic Analysis when Any One of the Observed Values is unknown

Abstract

If a periodic phenomena y shown by a function
is observed at six equidistant points throughout the period, the coefficients A₀, A₁, B₁, A₂ and B₂ can be determined by the method of harmonic analysis. But, when one of the observed values, y₁, for example, is unknown, the usual method can not be used. The author proposes a method of harmonic analysis for such a case. In this case' we may estimate graphically the unknown value, namely y₁", and with this estimated value togather with the observed values, we can determine the coefficients provisionally. From these coefficients we can calculate the value of y₁, and call it y₁". Then the true value of y₁, is given by the following equation,
Generally, when the periodic phenomena is shown by the function, above method is applied repeatedly, and the most probable value of y₁, may be determined.
Similarly, when one of the observed values at 2m equidistant points throughout the period of the function is unknown, the same method may be applied, and the most probable value of the unknown one is given by the equation