The Solution of Unsymmetrical-Sideband Problems with the Aid of the Zero-Frequency Carrier

Unsymmetrical-sideband problems are met in frequency modulation and single-sideband transmission. There has developed the urgent need of a simplified procedure for their solution. The "vector envelope" of a modulated signal is reviewed, with special attention to the simple cases of amplitude, phase, and frequency modulation, and of a single sideband. From this is developed the concept of the "zero-frequency carrier" with combined amplitude and angle modulation. The solution is valid for any carrier frequency much greater than the total width of sidebands in the signal, regardless of whether the carrier is present. It yields directly the envelope of the signal, as detected by a rectifier. It is applied to the general case of steady and transient modulation components. The simplified procedure is outlined in simple terms after rigorous derivation. It involves merely stating the input modulating signal relative to the zero-frequency carrier, putting it through the low-pass analog of the band-pass filter, and deriving the output modulating signal directly.