On pulse compression in dispersive media

A comparison between three methods used for the synthesis of suitable signals which result in pulse compression, when transmitted through dispersive media, is presented. These are the equalization of group-time delay method, the space-time rays method, and the matched-signal method. The three methods are shown to be equivalent if the signals are restricted to be frequency-modulated with uniform envelopes. A generalized expression for the requited frequency modulation law for pulse compression in an inhomogeneous dispersive medium is obtained. Considerations for lossy dispersive media and additional optimization of the signal envelope are also discussed.