A Cathode-Ray Method of Wave Analysis

Complex periodic functions, when transformed into a corresponding voltage wave, may be analyzed with the use of a cathode ray oscillograph. The complex wave is represented upon the fluorescent screen of the cathode ray tube by a vertical displacement at the same time that a sinusoidal horizontal oscillation exists. If the frequency of the sinusoidal oscillation bears an integral relation to the fundamental frequency of the complex wave, a Lissajous figure is viewed on the screen. The areas of these Lissajous figures are directly related to the coefficients of the Fourier series of the complex wave. The area is determined by measuring a photograph of the figure using a polar planimeter. The method is based on the theory developed by Mr. L. W. Chubb in connection with the Chubb Polar Analyzer.⁴ Advantages of the method are that it is quick and convenient, only standard laboratory equipment is necessary, and with special equipment, it promises to make possible the analysis of ultrahigh frequency waves.