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VIGRE seminar, summer 2000: Signal Analysis

Fran Narcowich
Students enrolled
Matt Riddle, (undergraduate mathematics student); John McDowell, (undergraduate physics student); Eric Bahuaud, Arturo Diaz, Sami Hamid, Adam Harbaugh, Troy Henderson, Trae Holcomb, Tzanio Kolev, Quoc Le Gia, Wuxiang Wu, (graduate mathematics students)
This seminar had the participation of the students in our REU Program. Signal analysis is the study of signals arising from either audio or video equipment. Several key applications of signal analysis were addressed.
A sound signal is often corrupted by noise (i.e., frequencies different from those in the desirable parts of the signal). Signal analysis can be used to filter out this unwanted noise. A Dolby filter, which filters out tape-hiss on cassette tapes, is an example along these lines.
Data Compression
Digitized audio and video signals are usually quite large, and are difficult to transmit electronically. Efficient transmission of these signals often requires compression, a process that eliminates the less significant parts of a signal. Compression is used, for example, in transmitting fingerprints from a police squad car to FBI Headquarters (in Washington, DC) to identify crime suspects.
Signals often have some feature that the user wants to detect. For example, the sound made by a mechanical device often changes when it does not operate correctly. A device that detects this change would be useful to the machine operator.
Fourier analysis and wavelets were two of the basic tools used to address the above applications. This seminar gave a brief overview of Fourier analysis techniques (e.g., FFT) and of wavelet analysis. Students then worked on projects associated with one of the above applications.