Sound visualizaation and manipulation: Theories and applications

There are many means to visualize sound in space and time. One could use many microphones or sensors that can effectively convert sound pressures to what we can use to visualize: for example voltage signals. How many such sensors and what kind of sensors’ configuration would be well enough to have sufficient information to visualize sound? The very first thing to answer this question is to define or choose what we do want to see: for example, a simple pressure-signal display, beamforming, or acoustic holography. These methods also have many different visualization expressions, depending on the mapping function between measurement domain and prediction or display domain. Therefore, the mapping entirely determines the information of display. On the other hand, if we want to make or manipulate sound in space and time, we may use loudspeakers instead of microphones. Then, our problem depends on what we want to make in space and time, instead of what we want to see in space and time. It has to be defined before we design our mapping function. If we want to reproduce sound field in the region of interest, then wave field synthesis (WFS) idea can be used. If we want to reproduce sound that is desired to be listened, then HRTF can be one of the functions. One may also attempt to design a tool that can make sound in space and time by neglecting what human hear or experience, then a quite different sound manipulation means can be introduced. In other words, depending on the way to define ‘3D sound,’ the function is to be selected and its performance is entirely determined by the function’s ability to map between two domains. Therefore, these two issues: sound visualization and manipulation can be seen, at least mathematical stand point, in terms of various mappings or basis functions. Our aim is to explore various basis functions for the visualization and manipulation and demonstrate how these function’s properties determine the quality of visualization and manipulation.