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lecture14 - EE313 Linear Systems and Signals Fall 2010 LTI...

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EE313 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 LTI System Analysis
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14 - 2 Zero-State LTIC System Response LTIC: Linear Time-Invariant Continuous-time System response = zero-input response + zero-state response Approaches to find the zero-state response Time-domain solutions to the differential equation Convolution in time domain: y ( t ) = f ( t ) * h ( t ) Continuous-time Fourier transform: Y ( ϖ ) = F ( ϖ ) H ( ϖ ) Laplace transform: Y ( s ) = F ( s ) H ( s )
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14 - 3 Example #1 Transfer function 1/( s +2) and input e -t u ( t ) Either way takes about the same amount of work ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 t u e e t y t u e e t y s s s s s F s H s Y j j j j F H Y s s H j s H H h(t) s s F j F t t t t j s Transform Inverse 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 output Calculate 2 1 2 1 Transform 1 1 1 1 input the Transform Transform Laplace By Transform Fourier By 2 2 - - - - = - = - = + - + = + + = = + - + = + + = = + = + = = + = + = ϖ ϖ ϖ ϖ
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