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Transfer functions of evanescent transmission channels are investigated in detail. Based on a Taylor expansion of the corresponding phase and attenuation constants, different characteristic transmission parameters are introduced (or revisited). The steady-state propagation of an RF carrier signal modulated by a narrowband base-band Gaussian pulse in evanescent waveguide sections is then studied. It is shown that temporal pulse compression as well as carrier frequency drift usually accompany such transmissions. It is also shown that under steady-state conditions, conventionally defined transmission velocities are not necessarily restricted to be less than or equal to c (speed of light in free space) as long as they are not related to direct measurements. Only the power coupling accompanying a measurement is responsible for limiting the transmission velocity of the measured physical quantity below or equal to c.