Background and Objective: This paper proposes a novel strategy to localize anomalies in the arterial network based on its response to controlled transient waves. The idea is borrowed from system identification theories in which wave reflections can render significant information about a target system. Cardiovascular system studies often focus on the waves originating from the heart pulsations, which are of low bandwidth and, hence, can hardly carry information about the arteries with the desired resolution. Methods: Our strategy uses a relatively higher bandwidth transient signal to characterize healthy and unhealthy arterial networks through a frequency response function (FRF). We tested our novel approach on data simulated using a one-dimensional cardiovascular model that produced pulse waves in the larger arteries of the arterial network. Specifically, we excited the blood flow from the brachial artery with a relatively high bandwidth flow disturbance and collected the subsequent pressure waveform at peripheral positions. To better differentiate FRFs of healthy and unhealthy networks, we used a FRF that removes the effects of heart pulsations. Results: Results demonstrate the ability of the proposed FRF to detect and follow-up on the development of a common carotid artery (CCA) stenosis. We tested distinct geometrical variations of the stenosis (size, length and position) and observed differences between the FRFs of healthy and unhealthy networks in all cases; such differences were mainly due to geometrical variations determined by the stenosis. Conclusions: We have provided a theoretical proof of concept that demonstrates the ability of our novel strategy to detect and track the development of CCA stenosis by using peripheral pressure waves that can be measured non-invasively in clinical practice.