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General formulas are developed for harmonic and total distortion in the frequency of the outputs of linear transmission systems with pure frequency-modulated inputs and with amplitude and phase characteristics involving wiggles that can be represented approximately by single sinusoidal functions of small amplitude. The amplitude wiggles represent departure from flatness, and the phase wiggles departure from linearity. This first-order analysis yields a result for total distortion D, which varies linearly with the amplitude of either wiggle if the amplitude of the other is made zero. It will be seen that D is periodic in the frequencies of the wiggles and in the audio frequency p and carrier frequency Â¿c of the frequency-modulated input. Of course, D is also a function of its index of modulation m. The formulas for D can be applied to amplifiers, filters, and the like in a communication system that satisfies the above assumptions. General distortion formulas are applied to waveguides loaded by pure resistances. Among other things, the so-called "long-line" effect in distortion is discussed. Graphs show the dependence of distortion on various parameters.