Microwave photonic systems are compelling for their ability to process signals at high frequencies and over extremely wide bandwidths as a basis for next generation communication and radar technologies. However, many applications also require narrow-band $(simtext{MHz})$ filtering operations that are challenging to implement using optical filtering techniques, as this requires reliable integration of ultra-high quality factor $(sim 10^8)$ optical resonators. One way to address this challenge is to utilize long-lived acoustic resonances, taking advantage of their narrow-band frequency response to filter microwave signals. In this paper, we examine new strategies to harness a narrow-band acoustic response within a microwave-photonic signal processing platform through use of light-sound coupling. Our signal processing scheme is based on a recently demonstrated photon-phonon emitter-receiver device, which transfers information between the optical and acoustic domains using Brillouin interactions, and produces narrow-band filtering of a microwave signal. To understand the best way to use this device technology, we study the properties of a microwave-photonic link using this filtering scheme. We theoretically analyze the noise characteristics of this microwave-photonic link, and explore the parameter space for the design and optimization of such systems.