solution for DTFT - Problem(1(a 1 1 5 2 ˆ 2 ˆ 2 ˆ 2 5 ˆ...

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Unformatted text preview: Problem (1) (a) ) ( ) ( 1 1 ]) 5 [ ] [ ( ) ( 2 / ˆ 2 / ˆ 2 / ˆ 2 / 5 ˆ 2 / 5 ˆ 2 / 5 ˆ ˆ 5 ˆ 4 ˆ ˆ ˆ ϖ ϖ ϖ ϖ ϖ ϖ ϖ ϖ ϖ ϖ ϖ j j j j j j j j n n j n n j j e e e e e e e e e e n u n u e X------ =- ∞-∞ =--- =-- = =-- = ∑ ∑ ) 2 / ˆ sin( ) 2 / 5 ˆ sin( ˆ 2 ϖ ϖ ϖ j e- = (b) ϖ ϖ ϖ ϖ ϖ ϖ α α α α α ˆ 8 ˆ 7 ˆ 7 ˆ ˆ ˆ 1 ) ( 1 ) ( ]) 8 [ ] [ ( ) ( j j n n j n n j n n n j n j e e e e e n u n u e X-- =- =- ∞-∞ =--- = = =-- = ∑ ∑ ∑ (c) ϖ α α α ϖ ϖ ϖ ϖ ∂ ∂ = =-- = ∑ ∑ ∑ =- =- ∞-∞ =- 7 ˆ 7 ˆ ˆ ˆ ) ( ) ( ]) 8 [ ] [ ( ) ( n n j n n j n n j n j e j e n e n u n u n e X 2 ˆ ˆ ˆ 8 8 ˆ 8 8 ˆ ˆ 8 ˆ ) 1 ( ) )( 1 ( ) 8 )( 1 ( 1 ) ( 1 ϖ ϖ ϖ ϖ ϖ ϖ ϖ ϖ j j j j j j j ce ce e c e c ce ce ce j--------- +- = -- ∂ ∂ = Problem (2) Using Taylor series or binomial expansion, m x ) 1 ( 1- can be expressed as ......
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This note was uploaded on 01/11/2011 for the course EE 4015 taught by Professor Shuhungleung during the Fall '10 term at City University of Hong Kong.

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solution for DTFT - Problem(1(a 1 1 5 2 ˆ 2 ˆ 2 ˆ 2 5 ˆ...

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