Distributed acoustic sensing (DAS) works as an efficient tool for monitoring acoustic signals in adverse environments, such as those commonly found in geophysical explorations, oil & gas, and military applications. DAS employs fiber-optic cables in order to record the acoustic wave impinging on them. These sensors can be several kilometers long, and its distributed capacity allows the acoustic wave to be measured with an adjustable space-frequency resolution. Recent DAS advances have shown that this technology is a formidable tool for implementing communication/telemetry systems in hostile environments. Notwithstanding the increasing practical interest in this technology, communication and signal processing communities have not concentrated proper efforts on addressing the myriad of challenges this technology raises. This paper bridges this gap by describing the basic signal model of a DAS system in a style compatible with the common background of these communities. It first derives, in an ideal setup, the relation between pressure signal and acquired baseband electric signals. The pressure signal is assumed to be a consequence of acoustic activity, whereas, the electric signals are obtained through the use of photodiodes which sense pressure-modulated light signals. The consequences of using long-pulse signals are also studied considering a simple continuous model for the reflections at different spatial regions of the fiber, called Rayleigh backscattering phenomenon. This paper includes results that compare the theoretical proposals with practical signals acquired in controlled experiments.