A Novel Approach for Finding the Spectrum of Periodically Modulated FM Carriers

A new technique for finding the frequency spectrum of a carrier frequency modulated by a periodic signal is presented. The technique is based on the frequency modulation (FM) equation due to Hess, which in the frequency domain is a double convolution equation. The technique reduces the FM spectrum problem to the solution of a set of linear equations in which the FM side-band amplitudes are the unknowns. The results obtained through this new technique can, in most cases, be obtained by other means. However, the technique is simple and as a result its implementation on a standard computer is both simple and fast. Furthermore, it is especially suitable when the modulating signal is in the form of a Fourier series with a large number of terms or requires a large number of terms to approximate it. Numerical results obtained using the technique for a large number of complex modulating signals are presented.