SOME_USEFUL_FORMULAS_and_TRANSFORMS

SOME_USEFUL_FORMULAS_and_TRANSFORMS - Some Useful Formulas...

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Unformatted text preview: Some Useful Formulas ∞ Φ X (u ) = −∞ ∞ ∫f X ( x)e dx iux 1 f X ( x) = 2π 1 RX (τ ) = 2π ∞ −∞ ∞ ∫Φ ∫S X (u )e −iux du (ω )eiωτ dω S X (ω ) = ∫ RX (τ )e − iωτ dτ −∞ X −∞ ∑ρ n =0 ∞ n = 1 , ρ <1 1− ρ 1 1 cos A cos B = cos( A − B) + cos( A + B) 2 2 1 1 sin A sin B = cos( A − B) − cos( A + B) 2 2 ∞ −∞ ∫ {δ ( x)}e iux dx = 1 ∞ ∫ 0 ∞ ⎛α ⎞ ⎧α n +1 n −αx ⎫ iux x e ⎬e dx = ⎜ ⎨ ⎜ α − iu ⎟ ⎟ n! ⎭ ⎩ ⎝ ⎠ n +1 , α > 0 ; n = 0, 1, … −∞ ∫ ⎧ ⎫ iux α −α u ⎨ ⎬e dx = e , 2 2 ⎩π (α + x ) ⎭ α >0 α − ∫α ⎧ ⎫ sin αu ⎪ 1 ⎪ iux ⎨ ⎬e dx = αu , ⎪ 2α ⎪ ⎩ ⎭ α >0 ...
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This note was uploaded on 01/07/2011 for the course ECE 166 taught by Professor Staff during the Spring '08 term at UCSD.

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SOME_USEFUL_FORMULAS_and_TRANSFORMS - Some Useful Formulas...

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