exercise - 1 例 nT t x t x = = A A t x 2 2<<<< t T...

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Unformatted text preview: 1 例 ) ( ) ( nT t x t x + = - = A A t x ) ( 2 / 2 / < <- < < t T T t ∑ ∞ = + + = 1 ) sin cos ( ) ( n n n t n b t n a a t x ϖ ϖ ] 2 ) 2 )( [( 1 ] [ 1 ) ( [ 1 2 / 2 / 2 / 2 / = + +- = +- = = ∫ ∫ ∫- - T A T A T Adt Adt T dt t x T a T T T T-T /2 t T /2- A A x ( t ) 例例例例例例 1 例例例例例例例例例例例例例例例例例例例例例例例例例例例例例例例例例 2 ∫ ∫ ∫- - +- = = 2 / 2 / 2 / 2 / ] cos cos [ 2 cos ) ( [ 2 T T T T n tdt n A tdt n A T tdt n t x T a ϖ ϖ ϖ 例例例例例例 t =- t , 例 ] cos ) 1 ( cos [ 2 2 / 2 / = +-- = ∫ ∫ T T n tdt n A tdt n A T a ϖ ϖ ∫ ∫ ∫-- +- = = 2 / 2 / 2 / 2 / ] sin sin [ 2 sin ) ( [ 2 T T T T n tdt n A tdt n A T tdt n t x T b ϖ ϖ ϖ 例例例例例例例例例 t =- t 例例 ∫ ∫ ∫ = +--- = 2 / 2 / 2 / ] sin 2 [ 2 ] sin ) 1 ( sin ) 1 ( [ 2 T T T n tdt n A T tdt n A tdt n A T b ϖ ϖ ϖ 3 =- =- = / 4 ) cos 1 ( 2 cos 1 4 2 / π π π ϖ ϖ n A n n A t n n T A b T n ⋅ ⋅ ⋅ = ⋅ ⋅ ⋅ = , 6 , 4 , 2 , 5 , 3 , 1 n n ∑ ∑ ∑ ∞ = ∞ = ∞ = = = = 1 1 1 sin 1 4 sin 4 sin ) ( n n n n t n n A t n n A t n b t x ϖ π ϖ π ϖ ) , 5 , 3 , 1 ( ⋅ ⋅ ⋅ = n tg 1 2 2 = = = + = = =- n n n n n n n b a b b a A a A ϕ ; ; ω A n ω 3 ω 例例例例例例例例例例例例例 5 ω 7 ω ω φ n ω 0 3 ω 0 5 ω 0 7 ω 0 π A 4 4 2 例例例例例例例例例例例例例例例例例例例例例例例例例例例例例例例例例-T /2 t T /2- A A x ( t ) - = A A t x ) ( 2 / 2 / < <- < < t T T t x ( t ) 例例例例例 a =0; a n =0 ∫ ∫ ∫ ∫ ∫ ∫ ∫ ∫ = + =- =- = + = +- = =--- 2 / 1 2 / 1 2 / 1 2 / 1 2 / 1 2 / 1 2 / 1 2 / 2 / 1 sin 4 ] sin sin [ 2 ] sin sin [ 2 ] sin sin ) ( [ 2 sin ) ( 2 T T T n T T T T T T n tdt n T A tdt n tdt n T A b dt dt t t tdt n tdt n T A tdt n A tdt n A T tdt n t x T b ϖ ϖ ϖ ϖ ϖ ϖ ϖ ϖ ;;;;; 5 ∑ ∑ ∑ ∫ ∞ = ∞ = ∞ =- =- = + + =- =- = = + = = = = = = =- =- =- =- = = 1 1 1 1 1 1 1 2 2 1 1 2 / 1 1 2 / 1 sin 1 4 ) 2 cos( 4 ) cos( ) ( 2 t ; ; ) , 6 , 4 , 2 ( ) , 5 , 3 , 1 ( 4 ) cos 1 ( 2 ) 2 2 cos 1 ( 2 4 ) 2 cos 1 ( 4 | cos 1 4 sin 4 n n n n n n n n n n n n n T T n t n n A t n n A t n A A t x a b g b b a A a a A n n n A n n A T T n Tn AT T n Tn A t n n T A tdt n T A b ϖ π π ϖ π ϕ ϖ π ϕ π π π π π ϖ ϖ ϖ ϖ ϖ ω A n ω 3 ω 5 ω 7 ω ω φ n ω 0 3 ω 0 5 ω 0 7 ω 0 π A 4 例例例例例例例例例例例例例 6 3 例例例例例例例例例例例例例例例例例例 -- = + + =- =- = = ± ± = = ± ± = ± ± =- =- = +- =-- = +-- =- + = +- = =--------------- ∫ ∫ ∫ ) , 3 , 1 ( 2 ) , 3 , 1 ( 2 2 tg Re Im tg ) , 3 , 1 ( 2 | | ) , 4 , 2 , ( ) , 3 , 1 2 ] cos 1 [ 1 )] ( 2 2 2 [ 1 2 ) 2 ( 1 2 ] 1 1 [ ] | 1 | 1 [ ] ) ( [ 1 ) ( 1 1 1 ) 2 ( 1 2 ) 2 ( 1 2 1 2 / 1 2 / 1 2 / 2 / 2 / 2 / 1 1 1 1 1 n n n A n n A X n n n A j n j n A e e j n A e e j Tn AT...
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exercise - 1 例 nT t x t x = = A A t x 2 2<<<< t T...

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