Some extensions of nyquist's telegraph transmission theory

The conditions necessary to achieve undistorted transmission of a pulse signal over a channel of finite bandwidth have been set down by Nyquist. These conditions are extended in this paper to eliminate the bandwidth restrictions. Conditions on the real and imaginary parts of the overall system characteristic which lead to the elimination of intersymbol amplitude and pulse width distortion are found. These generalized constraints do not depend on any sharp band limitation and permit one to find ideal conditions for band pass and gradual cutoff systems. The application of Nyquist's conditions usually amounts to equalizing the transmission characteristics in order to approximate an overall linear phase and some sort of symmetrical amplitude roll-off. This paper shows that the principles of channel shaping for distortionless transmission are a good deal more flexible than this. The application of this more general interpretation of Nyquist's theory is illustrated by several examples.