EECE 301 Discussion 06 - FT Examples

EECE 301 Discussion 06 - FT Examples - EECE 301 Signals...

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Unformatted text preview: EECE 301 Signals & Systems Prof. Mark Fowler Discussion #6 Fourier Transform Examples FT Examples Example: Find FT of x ( t ) given below: ) ( t x A A -2 2 t Solution: Note: ) ( 2 t Ap A ) 1 ( ) 1 ( ) ( : So 2 2 + = t Ap t Ap t x { } { } { } ) 1 ( ) 1 ( ) ( : y Linearit se 2 2 + = t p A t p A t x F F F { } j e P t p ) ( ) 1 ( : Shift Time se 2 2 = + F { } j e P t p = ) ( ) 1 ( 2 2 F [ ] j j e e AP X o = ) ( ) ( ... 2 = j e e j AP j j 2 2 ) ( 2 ) ( ) sin( 2 2 P j A = = sinc 2 ) ( : Table rom 2 P = sinc ) sin( 4 ) ( j A X Example Find FT of x ( t ) B 2 2 ) ( t x t Solution #1 1 1 1 ) ( 2 t p t Note: ( ) 2 ) ( ) ( ) ( 2 2 B t p t p t x = Verify it!! Using Convolution Property: ) ( 2 ) ( 2 2 P B X = From Table: = = sinc 2 2 2 sinc 2 ) ( 2 P = 2 sinc 2 ) ( ... B X So Solution #2 get to ) ( Take dt t dx dt t dx ) ( 2 B 2 B 2 2 t Take another derivative to get: dt t dx ) ( 2 2 B B 2 2 t 2 B Now by Linearity and & time shift: { }...
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This note was uploaded on 02/29/2012 for the course EECE 301 taught by Professor Fowler during the Fall '08 term at Binghamton University.

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EECE 301 Discussion 06 - FT Examples - EECE 301 Signals...

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