# lecture5 - EE 313 Linear Systems and Signals Fall 2010...

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Differential Equations 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

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5 - 2 n n n n n n n n n n n n n n n n n n ) ( on dependent zero are conditions initial all ) ( zero - non to response ) ( of t independen only conditions system internal from results 0 ) ( when response state - zero response input - zero response Total t x t x t x t x + = = Time-Domain Analysis For a system governed by a linear constant coefficient differential equation, Each component can be computed independently of other System satisfies linearity property if zero-input response is zero (i.e. all initial conditions are zero) Zero-state response is convolution of impulse x ( t ) y ( t )
5 - 3 Time-Domain Analysis Zero-input response Response when x ( t ) = 0 Results from internal system conditions only Independent of x ( t ) For most filtering applications (e.g. your stereo system), we want a zero-valued

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