lecture4 - Continuous-Time Convolution EE 313 Linear...

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Unformatted text preview: Continuous-Time Convolution EE 313 Linear Systems and Signals Fall 2010 Initial conversion of content to PowerPoint by Dr. Wade C. Schwartzkopf Prof. Brian L. Evans Dept. of Electrical and Computer Engineering The University of Texas at Austin 4 - 2 ( 29 ( 29 ( 29 ( 29 d t f f t f t f 2 1 2 1- - Convolution Integral Commonly used in engineering, science, math Convolution properties Commutative: f 1 ( t ) * f 2 ( t ) = f 2 ( t ) * f 1 ( t ) Distributive: f 1 ( t ) * [ f 2 ( t ) + f 3 ( t )] = f 1 ( t ) * f 2 ( t ) + f 1 ( t ) * f 3 ( t ) Associative: f 1 ( t ) * [ f 2 ( t ) * f 3 ( t )] = [ f 1 ( t ) * f 2 ( t )] * f 3 ( t ) Shift: If f 1 ( t ) * f 2 ( t ) = c ( t ), then f 1 ( t ) * f 2 ( t - T ) = f 1 ( t - T ) * f 2 ( t ) = c ( t - T ). Convolution with impulse, f ( t ) * ( t ) = f ( t ) Convolution with shifted impulse, f ( t ) * ( t-T ) = f ( t-T ) important later in modulation 4 - 3 Graphical Convolution Methods From the convolution integral, convolution is equivalent to Rotating one of the functions about the y axis Shifting it by t Multiplying this flipped, shifted function with the other function Calculating the area under this product Assigning this value to f 1 ( t ) * f 2 ( t ) at t ( 29 ( 29 ( 29 ( 29 d t f f t f t f- - 2 1 2 1 4 - 4 3 2 f ( ) 2-2 + t 2 + t g ( t- ) * 2 2 t f ( t )-2 2 3 t g ( t ) Graphical Convolution Example...
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This note was uploaded on 02/16/2011 for the course ECE 313 taught by Professor Evans during the Spring '11 term at University of Texas at Austin.

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lecture4 - Continuous-Time Convolution EE 313 Linear...

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