FT Tables_rev3

FT Tables_rev3 - Fourier Transform Table Time Signal 1 < t...

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Fourier Transform Table Time Signal Fourier Transform < < t , 1 ) ( 2 ω πδ ) ( 5 . 0 t u + j / 1 ) ( t u j / 1 ) ( + ) ( t δ < < , 1 real ), ( c c t real , c e c j 0 ), ( > b t u e bt 0 , 1 > + b b j , real o jt o e real ), ( 2 o o ) ( t p τ [ ] π τω 2 / sinc [] 2 / sinc t ) ( 2 p ) ( 1 2 t p t [ ] πω 4 / sinc 2 2 πτ 4 / sinc 2 2 t [ ] ) ( 1 2 2 p ) cos( t o [ ] ) ( ) ( o o + + ) cos( θ + t o [ ] ) ( ) ( o j o j e e ωω δω ωδπ + + ) sin( t o [ ] ) ( ) ( o o j + ) sin( + t o ()() jj oo je e θθ +−
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Fourier Transform Properties Property Name Property Linearity ) ( ) ( t bv t ax + ) ( ) ( ω bV aX + Time Shift ) ( c t x ) ( X e c j Time Scaling 0 ), ( a at x 0 ), / ( 1 a a X a Time Reversal ) ( t x real is ) ( if ) ( ) ( t x X X Multiply by t n , 3 , 2 , 1 ), ( = n t x t n , 3 , 2 , 1 ), ( = n X d d j n n n Multiply by Complex Exponential real ), ( o t j t x e o real ), ( o o X Multiply by Sine ) ( ) sin( t x t o [] ) ( ) ( 2 o o X X j ωω + Multiply by Cosine ) ( ) cos( t x t o ) ( ) ( 2 1 o o X X + + Time Differentiation , 3 , 2 , 1 ), ( = n t x dt d n n , 3 , 2 , 1 ), ( ) ( = n X j n Time Integration t d x λλ ) ( ) ( ) 0 ( ) ( 1 ωδπ X X j + Convolution in Time ) ( * ) ( t h t x ) ( ) ( H X Multiplication in Time ) ( ) ( t w t x ) ( * ) ( 2 1 π W X Parseval’s Theorem (General)
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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.

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FT Tables_rev3 - Fourier Transform Table Time Signal 1 < t...

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