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Unformatted text preview: Connexions module: m11541 1 Convolution - Complete example * Anders Gjendemsjø Richard Baraniuk This work is produced by The Connexions Project and licensed under the Creative Commons Attribution License † Abstract Shows a full example of convolution including math and gures. 1 Basic Example Let us look at a basic continuous-time convolution example to help express some of the important ideas. We will convolve together two square pulses, x ( t ) and h ( t ) , as shown in Figure 1 (a) (b) Figure 1: Two basic signals that we will convolve together. * Version 1.7: Jun 26, 2007 4:58 am GMT-5 † http://creativecommons.org/licenses/by/1.0 http://cnx.org/content/m11541/1.7/ Connexions module: m11541 2 1.1 Re ect and Shift Now we will take one of the functions and re ect it around the y-axis. Then we must shift the function, such that the origin, the point of the function that was originally on the origin, is labeled as point t . This step is shown in Figure 2, h ( t- τ ) . (a) (b) Figure 2: h (- τ ) and h ( t- τ ) . (a) Re ected square pulse. (b) Re ected and shifted square pulse....
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This note was uploaded on 02/15/2011 for the course SYSC 3600 taught by Professor Adsd during the Spring '10 term at Universidad Alfonso X El Sabio.
- Spring '10