Signal processing is a discipline that deals with the extraction of information from signals. The devices that perform this task can be physical hardware devices, specialized software codes, or combinations of both. In recent years the complexity of these devices and the scope of their applications have increased dramatically with the rapidly falling costs of hardware and software and the advancement of sensor technologies. This trend has made it possible to pursue sophisticated signal-processing designs at relatively low cost. Some notable applications, in areas ranging from biomedical engineering to wireless communications, include the suppression of interference arising from noisy measurement sensors, the elimination of distortions introduced when signals travel through transmission channels, and the recovery of signals embedded in a multitude of echoes created by multipath effects in mobile communications.
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Automata theory
A mathematical model of computing. The versatility of modern computers and their applications to the study of complex and dynamic systems, such as financial markets, cellular growth, and communication networks, raise questions about the ultimate power of computers. For example, what are the limitations, if any, on the tasks that we can ask computers to perform? Can we use computers to carry out any computational task we want? To answer such questions, we generally make use of abstract mathematical models. One of the most important mathematical abstract models that has been widely used to simulate objects and processes such as computer and digital circuits is automata theory. See also: Abstract data type; Computer
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Information theory
A branch of communication theory devoted to problems in coding. A unique feature of information theory is its use of a numerical measure of the amount of information gained when the contents of a message are learned. Information theory relies heavily on the mathematical science of probability. For this reason the term information theory is often applied loosely to other probabilistic studies in communication theory, such as signal detection, random noise, and prediction. See also: Electrical communications