A New Electrical Method of Frequency Analysis and Its Application to Frequency Modulation

A method of analyzing an arbitrary combination of sine wave voltages is described and the analysis of several examples carried out. The method is based on the appearance of certain figures, typical of definite frequency ratios, appearing in an oscillogram of the superposition of a constant frequency and a "search" voltage. The resolving power of the method is very high, allowing component voltages of only two cycles per second frequency difference to be clearly resolved. A frequency modulated wave is then analyzed and the spectrum representation f(t)=n-0 J
n
(Δf/α) sin 2π(f+nα)t found to hold under the approximate conditions Δf0
/10, α0
/10. The consequences of the periodicity or nonperiodicity which can occur with relatively large Δf and α is discussed. A simple expression for the spectrum of a wave with both amplitude and frequency modulation is derived, which allows an immediate oversight of the changes in side band magnitude occurring when one type of undesired modulation accompanies the other. Finally, the relation of the oscillogram of superposed constant frequency and search voltages to Lissajous figures is pointed out, and a comparison with diatonic harmony made.