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_Signal_FAQ22_Summary - Signal x t = F-1 Spectrum X f = X f...

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Signal Spectrum ( 29 ( 29 { } ( 29 - - = = df e f X f X t x t j ϖ 1 F ( 29 ( 29 { } ( 29 - - = = dt e t x t x f X t j ϖ F ( 29 ( 29 [ ] = = t x t x 1 1 real ( 29 ( 29 [ ] - = f X f X 1 1 ( 29 ( 29 f X f X - = = 1 1 symmetric ( 29 [ ] ( 29 [ ] f X f X - - = - = 1 1 arg symmetric anti arg ( 29 ( 29 ( 29 12 12 2 2 2 by delayed t x t x t y = - = ( 29 ( 29 f X e f Y j 2 12 2 ϖ - = ( 29 ( 29 times expanded 13 13 3 3 3 t x t x t y = = ( 29 ( 29 f X f Y 13 13 3 3 = ( 29 ( 29 t x dt d t y 4 4 = ( 29 ( 29 f X j f Y 4 4 ϖ =
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Signal Spectrum ( 29 ϖ j f X + = 15 1 5 ( 29 ( 29 = = - - elsewhere , 0 0 , 15 15 5 t e t u e t x t t t 0 t e 15 - ( 29 ( 29 ( 29 ( 29 f f f f X sinc sin 6 = = π π 1 f 1 - 1 ( 29 ( 29 t t x sinc 7 = 1 t 1 - 1 ( 29 ( 29 t t x rect 6 = t 5 . 0 - 1 5 . 0 ( 29 ( 29 f f X rect 7 = f 5 . 0 - 1 5 . 0
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Signal Spectrum ( 29 [ ] 1 F = t δ f 1 ( 29 t δ t 0 1 Area t 0 1 1 Area 0 ( 29 f δ f 0 1 Area t 1 ( 29 [ ] t j e f 0 2 1 1 F π δ = = - ( 29 3 - f δ f 3 1 Area ( 29 [ ] t j e f 3 2 1 3 F π δ = - - t 0 3 - 3 6 1 f 0 3 1 3 1 ( 29 ( 29 ( 29 ( 29 4 4 cos 4 cos 4 - = - t e t t e j jt δ δ
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Signal Spectrum ( 29 ( 29 ( 29 ( 29 ( 29 - - = = ' ' ' * 1 1 1 1 1 dt t t h t x t h t x t y ( 29 t h 1 ( 29 t x 1 ( 29 ( 29 ( 29 f H f X f Y 1 1 1 = ( 29 f H 1 ( 29 f X 1 ( 29 ( 29 ( 29 t h t x t y 2 2 2 = ( 29
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