EECE253_06_FourierTransform

EECE253_06_FourierTransform - EECE\CS 253 Image Processing...

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Unformatted text preview: EECE\CS 253 Image Processing Richard Alan Peters II Department of Electrical Engineering and Computer Science Fall Semester 2011 Lecture Notes Lecture Notes: The 1&2-Dimensional Fourier Transforms This work is licensed under the Creative Commons Attribution-Noncommercial 2.5 License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc/2.5/ or send a letter to Creative Commons, 543 Howard Street, 5th Floor, San Francisco, California, 94105, USA. 12/06/11 2 1999-2011 by Richard Alan Peters II Signal: A measurable phenomenon that changes over time or throughout space. 01101000101101110110010110001 01101000101101110110010110001 sound image code 12/06/11 3 1999-2011 by Richard Alan Peters II Signals: Space-Time vs. Frequency- Domain Representation Space/time representation: a graph of the measurements with respect to a point in time and/or positions in space. Fact: signals undulate (otherwise theyd contain no information). Frequency-domain representation: an exact description of a signal in terms of its undulations. 12/06/11 4 1999-2011 by Richard Alan Peters II Origin of Sounds The mechanical vibrations of an object in an atmosphere. Vibrations: internal elastic motions of the material. The surface of the object undulates causing compressions and rarefactions in the air which propagate through the air away from the surface. An object vibrates with different modes . A mode is a vibratory pattern with a distinctive shape part of the object surface moves out while another part moves in a standing wave . 12/06/11 5 1999-2011 by Richard Alan Peters II Vibratory Modes / Standing Waves: Examples displacement from rest position string modes internal pressure pipe modes Note that the negatives of these also will occur Note that the negatives of these also will occur Note that the modes are all sinusoids. Note that the modes are all sinusoids. 12/06/11 6 1999-2011 by Richard Alan Peters II Sound Waves: string sound pipe sound Emerge from the superposition of the modes. 12/06/11 7 1999-2011 by Richard Alan Peters II Sound Waves: string sound pipe sound Emerge from the superposition of the modes. The vibratory modes add up to one complex motion that pushes the air around the vibrating object The vibratory modes add up to one complex motion that pushes the air around the vibrating object Even-order harmonics Even-order harmonics Odd-order harmonics Odd-order harmonics 12/06/11 8 1999-2011 by Richard Alan Peters II Fact: Any Real Signal has a Frequency-Domain Representation The modes shown (blue) sum to the rippling square wave (black)....
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This note was uploaded on 12/06/2011 for the course EECE 253 taught by Professor Alanpeters during the Summer '07 term at Vanderbilt.

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EECE253_06_FourierTransform - EECE\CS 253 Image Processing...

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