ConvolutionLecture

ConvolutionLecture - Graphical Convolution Linear Systems...

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Unformatted text preview: Graphical Convolution Linear Systems and Signals – Lecture 7 Dr. J. K. Aggarwal The University of Texas at Austin Graphical Interpretation of Convolution ¡ Definition: ¡ For a causal system with causal input, 1 2 1 2 2 1 ( ) ( ) ( ) ( ) ( ) ( ) x t x t x x t d x x t d τ τ τ τ τ τ ∞ −∞ ∞ −∞ ∗ = − = − ∫ ∫ ( ) ( ) ( ) ( ) ( ) ( ) t t x t h t x h t d h x t d τ τ τ τ τ τ ∗ = − = − ∫ ∫ τ ( ) x τ τ ( ) h t τ − t An Example Impulse Response ( ) h t t → Input signal t → ( ) x t An Example ...contd τ τ → ( ) x τ τ → ( ) h τ τ → ( ) x τ − Mirror image about the y-axis For each t , multiply and compute area under the curve Convert to functions of Slide! τ → ( ) x t τ − t An Example …contd ( ) ( ) x t h τ τ − τ → t Product Find the product and integrate Plot the value of y(t) Repeat the process for every value of t t → ( ) y t t An Example ...contd Impulse Response ( ) h t t → Input signal t → ( ) x t ( ) t e u t − 20 5 10 An Example...
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This note was uploaded on 02/08/2011 for the course EE 313 taught by Professor Cardwell during the Spring '07 term at University of Texas.

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ConvolutionLecture - Graphical Convolution Linear Systems...

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