CheatSheet4

CheatSheet4 - orthogonalization): Integration by parts: 1 1...

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Trigonometric Fourier Series: Compact Trigonometric Fourier Series Exponential Fourier Series Convolution ) ( ) ( ) ( t x t h t y = = τ d t x h t y ) ( ) ( ) ( Trig Identities: {} {} {} () () x x x x A A A A A A A A A B A B A B A B A B A B A B A B A B A B A B A B A B A B A B A sin 2 cos cos 2 sin 1 cos sin 2 cos 2 1 2 1 cos 2 cos 2 1 2 1 sin cos sin 2 2 sin ) sin( ) sin( 2 1 cos sin ) cos( ) cos( 2 1 cos cos ) cos( ) cos( 2 1 sin sin sin sin cos cos ) cos( sin cos cos sin ) sin( 2 2 2 2 m m = ± ± = ± = + + = = = + + = + + = + = = ± ± = ± π = = + + = 1 0 1 0 0 ) sin( ) cos( ) ( n n n n t n b t n a a t f ω −∞ = = n t jnw n e D t f 0 ) ( = 0 ) ( 1 0 0 T dt t f T a = 0 ) cos( ) ( 2 0 0 T n dt t nw t f T a = 0 ) sin( ) ( 2 0 0 T n dt t nw t f T b = + + = 1 0 0 ) cos( ) ( n n n t n C C t f θ 0 0 a C = 2 2 n n n b a C + = ⎛ − = a b n 1 tan j e e e e j e dt e t f T D j j j j j T t jn n 2 sin 2 cos sin cos ) ( 1 0 0 0 = + = + = =
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Basis Functions (Gram-Schmidt
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Unformatted text preview: orthogonalization): Integration by parts: 1 1 = f 1 1 , 2 2 2 + = f 1 1 , 3 2 2 , 3 3 3 + + = f 1 1 1 2 1 , 2 f f f = 2 2 2 3 2 , 3 f f f = 1 1 1 3 1 , 3 f f f = = vdu uv udv...
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This note was uploaded on 06/08/2009 for the course BME 513 taught by Professor Yen during the Spring '07 term at USC.

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CheatSheet4 - orthogonalization): Integration by parts: 1 1...

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