_Signal_FAQ22_Summary - Signal Spectrum 29 29 29 ∞ ∞...

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Unformatted text preview: 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 = Signal Spectrum ( 29 ϖ j f X + = 15 1 5 ( 29 ( 29 ≥ = =-- elsewhere , , 15 15 5 t e t u e t x t t t 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 .- 1 5 . ( 29 ( 29 f f X rect 7 = f 5 .- 1 5 . Signal Spectrum ( 29 [ ] 1 F = t δ f 1 ( 29 t δ t 1 Area t ∆ 1 1 Area → ∆ ( 29 f δ f 1 Area t 1 ( 29 [ ] t j e f 2 1 1 F π δ = =...
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This note was uploaded on 08/02/2009 for the course ECE EE2009 taught by Professor Prof.c.c.ko during the Fall '07 term at National University of Singapore.

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_Signal_FAQ22_Summary - Signal Spectrum 29 29 29 ∞ ∞...

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