Spectral Characteristics of FDM-FM Signals

The power spectrum of a sinusoidal carrier which is frequency modulated by a normally distributed baseband signal may be expanded as a sum of weighted convolution terms. The significant parameter in the expansion, for an ideally bandlimited baseband spectrum, isRₓ(0) = Rẋ(0)/fminfmax whereRẋ(0)is the mean squared frequency deviation andfmin andfmax are the lower and upper frequency limits of the baseband spectrum. For small values ofRₓ(0), the spectrum may be approximated using the baseband and the carrier. For largeRₓ(0), the spectrum is asymptotically Gaussian. We have computed spectra on a digital computer for intermediate values ofRₓ(0). In all computations, the spectra are approximated by ten convolution terms, defining the carrier component as the first term. Computations are forRₓ(0) = 1, 2, 3, 4, 5for a rectangular baseband spectrum with no pre-emphasis and with CCIR pre-emphasis. The results are for typical multichannel FDMFM bands 12 to 36 kHz, 12 to 60 kHz, 12 to 156 kHz, and 12 to 252 kHz.