Reflectometry is a structural health monitoring technique that allows to efficiently detect and localize electrical defects in wire networks. The main challenge in reflectometry is to improve the precision of defect localization and characterization, especially in the case of complex networks. Thesolution is to increase the frequency of the injected signal since the spatial resolution is inversely proportional to theinjected signal frequency. However, such solution applicability is limited by the sampling capabilities of existing Analog-to-Digital Converters (ADC). In this paper, we propose a sampling approach based on Compressive Sensing (CS) in the context of reflectometry. The resulting methodology offers the possibility to inject high frequency signals and later to reconstruct the reflected waveform from a lower set of samples than that required in the classical sampling scheme. In that respect, a complex linear chirp signal is considered as a testing signal and injected in a complex Y-branches network with a hard defect at the edges. In order to have a sparse representation, the reflected chirp signal is decomposed in the Fractional Fourier Transform (FrFT) domain. The main result is that the new acquisition scheme allows the detection of multiple reflection peaks caused by the defects at a sampling frequency 10 times lower than the actual sampling rate with a relative fault location error of 2%