Reflectometry is a diagnostic technique that allows detection and localization of defects in cables. Analog-to-Digital Converters (ADC) are one of the most required components in the architectures of reflectometry systems. However, the respect of the sampling theorem and the need of performing real-time analysis restrict the highest frequency of the injected signals and thus preclude the detection of some kinds of defects. The contribution of this paper is to introduce an alternative ADC based on compressive sensing of the reflected signal in order to overcome the limits of Nyquist and to reduce memory storage. For this, a complex linear chirp signal is injected in the wires, a dictionary of sparsity based on fractional Fourier transform is used and a Random Demodulator is employed as an analog encoder. The main result is that the new ADC scheme allows to reconstruct the reflectogram with a sampling frequency of Nyquist limit.