Date of Award


Document Type


Degree Name

Master of Science


Department of Mathematics and Statistics

First Advisor

Mark E. Oxley, PhD


Signal processing is the method of taking a given signal and extracting useful information, usually by a means of a transformation of some kind. Acoustic signals are functions of time in which the output is a pressure or a velocity potential response. An acoustic signal is affected by the environment in which it propagates, so one can attempt to remove the environmental effects to extract the useful information, in this case the original signal. This thesis will derive, in a mathematical framework, the process of filtering extraneous signals in a way that yields the original signal, and will then apply this process to the Cocktail Party Problem in an attempt to describe how useful this ability can be. This ability has many applications in both the Department of Defense and commercial industries. Considering an acoustic signal to be a form of information, the basic purpose of filtering the received signal is to retrieve the original information, such as in intelligence gathering. The private sector also has many uses for this method. Consider a boardroom meeting transpiring in a room. While at most times, there will only be one person talking, there may be at other times many people talking at once, arguing with each other. This is when the application of this signal processing will become most useful. An acoustic signal can be distorted in a number of ways by an environment, thereby making information contained within the signal less accessible. The effect of the environment must be determined to retrieve the original information. This thesis pursues those goals by finding solutions to the following three problems: finding and inverting the room transfer function, filtering different signals being transmitted at once, and retrieving the signal of a mobile source.

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