2025-L16su09 - ECE2025 Summer 2009 Lecture 16...

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1 6/30/2009 1 ECE2025 Summer 2009 Lecture 16 Continuous-Time Convolution 1 Jul 09 6/30/2009 3 ANNOUNCEMENTS ± Do Lab 7 on July 1-2 ± Done mainly in lab, shorter report than usual ± HW #7 due July 6-7 ± Lots of complicated material on this HW ± Do not procrastinate starting it! ± No classes on July 3 ± Next week: lectures W and F (July 8,10) ± Recitations as usual ± Quiz 3 Monday July 13 6/30/2009 4 Linear and Time-Invariant (LTI) Systems ± If a continuous-time system is both linear and time- invariant, then the output y(t) is related to the input x(t) by a convolution integral convolution integral where h(t) is the impulse response impulse response of the system. = = ) ( ) ( ) ( ) ( ) ( t h t x d t h x t y τ 6/30/2009 5 Convolution of Impulses, etc. ± Convolution of two impulses ± Convolution of step and shifted impulse ± Convolution of step and derivative of impulse = ) ( ) ( 2 1 t t t t δ ) ( 2 1 t t t = ) ( ) ( 0 t t t u ) ( 0 t t u u ( t ) ∗δ (1) ( t ) = ( t )
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2 6/30/2009 6 General Convolution Example ) ( 0 0 0 0 0 0 ) ( ) ( ) ( ) ( ) ( ) ( ) ( 0 ) ( t u a b e e t t b a e e t t d e e e d t u e u e t h t x d t h x t y bt at bt at t b a bt t b a = < > + = < > = = = = τ ) ( ) ( t u e t x at = a b t u e t h bt = ), ( ) ( 6/30/2009 7 Evaluating a Convolution = = ) ( ) ( ) ( ) ( ) ( t x t h d t x h t y ) ( ) ( t u e t h t = ) 1 ( ) ( = t u t x 6/30/2009 8 “Flipping and Shifting” ) ( x g ( ) = x ( ) = u ( 1) g ( t ) = x ( ( t )) = x ( t ) “flipping”
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This note was uploaded on 01/24/2010 for the course ECE 2025 taught by Professor Juang during the Spring '08 term at Georgia Institute of Technology.

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2025-L16su09 - ECE2025 Summer 2009 Lecture 16...

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