Linear Signal Stretching in a Time-Variant System

Limitations of present techniques, such as sampling, dictate the consideration of new approaches to the display of nanosecond waveforms. Some thoughts about a novel method of observing nanosecond pulses that might be nonperiodic are discussed. The basic idea hinges on a stretching operation that transforms a given waveform
f(t)
into
(r \alpha)f( \alpha t)
. After sufficient stretching one can observe the waveform on a conventional oscilloscope. A mathematical analysis precedes several suggestions for realizing the required system. One of the more interesting of these consist of a delay line whose velocity of propagation is made to vary with time, simultaneously along the entire length of the line, according to a given relationship. The suggested method may also be used advantageously in pulse-compression applications.