MATH-603 Signal Processing
Spring for 2016-2017
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Description. The acquisition of analog signals (such as live music, electrocardiograms, cellular telecommunications, and live video) and the digital representation of these signals (in formats such as MP3 and AVI) forms the foundation of numerous advanced applications. For example, live streaming video from a cellular phone involves the fast acquisition of high-fidelity analog images and audio which must be then converted to compressed digital formats. The resulting digital files are then encoded as analog wireless signals and tranferred wirelessly to cellular towers. All these steps occur before the video reaches the internet, and at each step of this process, several Signal Processing techniques are utilized to ensure the quality of the final product.

This course covers analog to digital conversion, digital to analog conversion, linear filters, Fourier transforms, convolutions, the Nyquist sampling theorem, and applications of Signal Processing to audio processing and wireless telecommunications. Information theoretic aspects of communications are also discussed, culminating in an introduction to the Shannon-Hartley theorem regarding capacity of a noisy communications channel. Given sufficient time and student interest, we also provide an introduction to recent field of Compressed Sensing, which provides theory and algorithms to support sampling below the classical Nyquist rate. Prereqs Math 501, 502.

Textbooks.
Digital Signal Processing: A Practical Guide for Engineers and Scientists, 1st Edition, by Steven Smith

Schaums Outline of Digital Signal Processing, 2nd Edition, by Monson Hayes

Restrictions:
Must be enrolled in one of the following Levels:
MN or MC Graduate
Must be enrolled in one of the following Majors:
Mathematics and Statistics

Credits: 3
Prerequisites: Math 502, Math 503
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