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The output spectrum of an idealized version of a reentrant delay line speed-up device is calculated. Study of this spectrum yields considerable insight into the rather peculiar way in which this device achives a speed-up in real time. The analysis is then modified to show the effects of time sampling and boxcarring on the output spectrum. Finally, the use of digital instead of analog delay lines is discussed, and an expression for the power density spectrum of the output quantization noise is derived.