Lecture 4 Lecture Topics - dt t dy t y s sY s X s sH s sX s...

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Lecture 4. Lecture Topics ECSE-2410 Signals & Systems (Wozny) Spring 2011 Fri 02/04/11 1. Review. How to handle special Partial Fraction Expansion cases: (a) () 1 + = s s s H (b) () () 1 + = s s e s H s 2. Definition of (a) Causality (Text 1.6.3) (b) Linearity (Text 1.6.6) (c) Time-Invariance (Text 1.6.5) Is linear? T I ? What about () () t x t y 2 = ( ) ( ) ( ) t x t K t y = ? 3. LTI Properties: () t x a () t y a () () t x t x 2 1 + () ( ) t y t y 2 1 + () 0 t t x () 0 t t y () dt t dx () dt t dy () ττ d x t () d y t Verify derivative property. Suppose () () () s X s H s Y = L e t () () () () s sX s X dt t dx t x = = 1 1 T h e n () () () () () ( ) () () () ()
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Unformatted text preview: ( ) dt t dy t y s sY s X s sH s sX s H s X s H s Y = ↔ = = = = 1 1 1 Is flip LTI Invariant? Suppose ( ) ( ) ( ) s X s H s Y = L e t ( ) ( ) ( ) ( ) s X s X t x t x − = ↔ − = 1 1 T h e n ( ) ( ) ( ) ( ) ( ) s X s H s X s H s Y − = = 1 1 Stuck! ∴ Not True! 4. Superposition Consider ( ) ( ) t u t x = ( ) ( ) ( ) ( ) t u e t s t y t − − = = 1 ( ) 1 1 = s + s H ( ) t x 1 Find output when input is 1 5. Convolution Integral. See Note 103. (Text 2.2) t 1 0...
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This note was uploaded on 10/22/2011 for the course ECSE 2410 taught by Professor Wozny during the Spring '07 term at Rensselaer Polytechnic Institute.

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