To successfully achieve our goal of replicating selective hearing, there were several decisions regarding limitations and simplifying assumptions that we had to make. Time and mathematical simplicity were the two principle reasons for our decisions.
First, we faced equipment limitations. We opted to use a single, 16-element array because several projects utilizing multiple microphone arrays have already been completed; we therefore took the opportunity to further investigate the design parameters of a single array.
Second, we had to make assumptions pertaining to the bandwidth of our sound signals (narrowband vs. broadband). Because human speech is composed of many different frequencies, it is obvious that most real-world applications of selective hearing involve broadband signals. However, we elected to operate upon pure tones, which allowed us more time todedicate to investigating methods of replicating selective hearing as well as optimizing design parameters of the microphone array.
Third, we decided to decrease the degrees of freedom allowed for our sound sources. In other words, we decreased the number of directions in which the incoming sound signals is allowed vary. There are two directional degrees of freedom in three-dimensional space: azimuth angle and elevation angle. We decided to simplify our project by holding elevation constant at 0, and only varying the azimuth angle.
Finally, we decided to assume that the azimuth angles of incoming signals are known a priori. In previous semesters, projects which triangulate the position of a sound source using microphone array beamforming have already been completed. We decided that implementing an original triangulation scheme was redundant, and would have prevented us from focusing on designing something original.