Harmonie analysis by direct area measurements

ANY PERIODIC function can be expressed as a Fourier series, a summation of sinusoidal terms having frequencies which are integral multiples of the fundamental frequency. The most direct method of determining the coefficient of any term consists basically of determining the net area, over one full cycle, of a curve which is the product of the function and a unit sine-wave of the desired frequency. No matter what the appearance of the product curve, the net area will be exactly the same as that which would be produced by the in-phase component of the desired harmonic multiplied by a unit sine wave of the same frequency. The procedure is repeated with a unit cosine wave and the two components combined in quadrature.