An Optical Harmonic Analyzer

P E R I O D I C function can be represented for all values of the variable by a Fourier Series. A function which is not periodic can be so represented between any finite limits, although the series may be entirely unlike the function beyond these limits. If a function is approximately periodic, the Fourier Series representing adjacent portions of it will generally be approximately alike. Although in general an infinite number of terms is required to represent a function exactly, it is common experience that a great many functions of practical interest can be closely approximated by a series of from ten to thirty terms.2 PRINCIPLE OF OPERATION The principle of this analyzer was suggested by E. C. Wente of these Laboratories.3 It may be outlined as follows. The Fourier Series expansion of a function is given by either of the following equivalent expressions.4 * Presented at Meeting of Acoustical Society of America, Washington, D. C., M a y 3, 1938. 1 For comparison, analysis to 30 harmonics on the Henrici type instrument requires five or six hours. A resonance analyzer, such as the vibrating reed type, can complete an analysis in a few seconds, but the phases will not be given, and if the function is provided in graphical form it must be converted into an electrical or acoustic wave form repeated enough times for the resonant elements to reach a steady state response. 2 A description of a number of the more important methods of harmonic analysis, together with a bibliography, is contained in " S o u n d Analysis," H.