This dissertation proposes a miniature FIR filter that works at microwave frequencies, whose filter response can ideally be digitally programmed. Such a frequency agile device can find applications in cellular communications and wireless networking. The basic concept of the FIR filter utilizes a low loss acoustic waveguide of appropriate geometry that acts as a traveling wave tapped-delay line. The input RF signal is applied by an array of capacitive transducers at various locations on the acoustic waveguide at one end that excites waves of a propagating acoustic mode with varying spatial delays and amplitudes which interfere as they propagate. The output RF signal is picked up at the other end of the waveguide by another array of capacitive transducers. Tuning of the FIR filter coefficients is realized by controlling the DC voltage profile applied to the individual transducers which essentially shapes the overall filter response. Equivalent circuit modeling of the capacitive transducer, acoustic waveguide and transducer-line coupling is presented in this dissertation. A theoretical model for the filter is developed from a general theory of an array of transducers exciting a waveguide and is used to obtain a set of filter design equations. A MATLAB based circuit simulator is developed to simulate the filter responses. Design parameters and simulation results obtained for an example waveguide structure are presented and compared to the values estimated by the theoretical model. A waveguide structure utilizing the Rayleigh-like mode of a ridge is then introduced. A semi-analytical method to obtain propagating elastic modes of such a ridge waveguide etched in an anisotropic crystal is presented. Microfabrication of a filter based on ridges etched in single crystal Silicon is discussed along with details of the challenges faced. Finally, future work and a few alternative designs are presented that can have a better chance of success. Analysis and modeling work to this point has given a good understanding of the working principles, performance tradeoffs and fabrication pitfalls of the proposed device. With the appropriate acoustic waveguide structure, the proposed device could make it possible to realize miniature programmable FIR filters in the GHz range.