lti-review

# lti-review - B o s t o n U n i v e r s i t y D e p a r t m...

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Unformatted text preview: B o s t o n U n i v e r s i t y D e p a r t m e n t o f E l e c t r i c a l a n d C o m p u t e r E n g i n e e r i n g E C 5 5 S T O C H A S T I C P R O C E S S E S N o t e s o n L T I I n p u t / O u t p u t R e l a t i o n s h i p s f o r S i n g l e- I n p u t / S i n g l e- O u t p u t S y s t e m s D e t e r m i n i s t i c C a s e h ( t ) y ( t ) x ( t ) C o n t i n u o u s T i m e D i s c r e t e T i m e S i g n a l s B L T : X ( s ) = R ∞- ∞ x ( t ) e- s t d t B Z T : X ( z ) = ∑ ∞ n =- ∞ x ( n ) z- n C T F T ( R a d i a n s ) : X ( j ω ) = R ∞- ∞ x ( t ) e- j ω t d t D T F T ( R a d i a n s ) : X ( e j ω ) = ∑ ∞ n =- ∞ x ( n ) e- j ω n C T F T ( H e r t z ) : X ( f ) = R ∞- ∞ x ( t ) e- j 2 π f t d t D T F T ( H e r t z ) : X ( f ) = ∑ ∞ n =- ∞ x ( n ) e- j 2 π f n I C F T : x ( t ) = 1 2 π R ∞- ∞ X ( j ω ) e j ω t d ω I D F T : x ( n ) = 1 2 π R π- π X ( e j ω ) e j ω t d ω = R ∞- ∞ X ( f ) e j 2 π f t d f = R 1- 1 X ( f...
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## This note was uploaded on 09/29/2009 for the course EC 505 taught by Professor Karl during the Fall '04 term at BU.

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