20085ee102_1_F08-102-HW-7

20085ee102_1_F08-102-HW-7 - FALL 2008: Put First Letter of...

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Put First Letter of LAST Name in the corner →→± ( Otherwise Your HW May Be LOST! ) PRINT: (LAST , Middle, First):——————————————————– HW: # 7 1 A LATE HW CANNOT BE A HW! Posted: W, November 19 Hand In To Me: M, December 1 Attach This Sheet To Your HW (Otherwise It May Be Lost!) The following Table lists Basic Properties of FT. The t -domain (on your left – L) is separated from the ω -domain (on your right – R) by “ | ”. You can show L implies R or R implies L by using the integrals on the second line of the Table. If you know a proof going from L to R, you may want to go from R to L to see whether you can get the same result. Basic Properties of FT f ( t ) := F - 1 { F ( i ω ) } ←- | -→ F ( i ω ) := F{ f ( t ) } f ( t ) = 1 2 π ± -∞ e i ω t F ( i ω ) d ω := F - 1 { F ( i ω ) } | F ( i ω ) = ± -∞ e - i ω t f ( t ) dt := F{ f ( t ) } 1. Linearity : af 1 ( t ) + bf 2 ( t ) | aF 1 ( i ω ) + bF
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20085ee102_1_F08-102-HW-7 - FALL 2008: Put First Letter of...

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