A Fourier Series Experiment

An experiment is described illustrating the fact that an approximand to a periodic function in the form of a truncated Fourier Series minimizes the mean-squared error. The experiment is implemented on an analog computer wherein the first three components of a periodic wave are generated and their amplitudes (and phases to a certain extent) are adjusted to minimize the squared-error integrated over one period. Sources of error are discussed briefly, and experimental technique is outlined. Verification of the principle of minimization is obtained to within a few percent in all cases.