Distortion-Band-Pass Considerations in Angular Modulation

The distortion introduced into an angular modulated signal transmitted through a network or medium is analyzed using the sideband approach. An exact open-form solution of the output signal is derived; however, the usefulness of this equation is limited by the ability to perform the indicated integrations. It is shown that exact solutions may readily be found for transfer functions which are linear exponential functions of frequency, and since over a given frequency interval, any transfer function may be expanded in an orthogonal set of linear exponential functions of frequency, a solution is always obtainable. A few examples of possible transfer functions are treated, illustrating the distortion tendencies for both the amplitude and phase characteristics. A rule-of-thumb formula is derived to determine the maximum undistorted modulation frequency which may be transmitted through a network of a given band-pass characteristic. It is concluded that linear phase characteristics are a more important design objective than flat amplitude characteristics in minimizing distortion.