102_1_Week-10-Recap

102_1_Week-10-Recap - 48 NHAN LEVAN WEEK 10 RECAP 4 P13....

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Unformatted text preview: 48 NHAN LEVAN WEEK 10 RECAP 4 P13. Let sig t := 1 , t , (sig := signum) :=- 1 , t < Then F{ sig t } =? SOLS: Please plot the signal 2 U ( t )- 1 Then you will see that sign t = 2 U ( t )- 1 F{ sign t } = F{ 2 U ( t )- 1 } F{ sign t } = 2 ( ) + 2 i - 2 ( ) = 2 i Note: Here F{ sig t } is computed in terms of F{ U ( t ) } . Hence one can also find F{ U ( t ) } in terms of F{ sig t } ? For this you only have to note that d dt sig t = 2 ( t ) F{ 2 ( t ) } = F{ d dt sig t } = i F{ sigt } Therefore F{ sig t } = 2 i F{ U ( t ) } = 1 2 F{ 1 + sigt } = 1 2 { 2 ( ) + 2 i } ( HaHa ) 26. UNIFORM SAMPLING We begin with a simple Problem. P14. Consider the pair: ( - Band-Limited) sin t t , t R | rec ( , ) , [- , ] Now let us define the LTI system denoted LP whose IRF is (26.1) h ( t ) := sin t t , t R then LP is clearly non-causal. Hence it is called an Ideal Low Pass Filter (or system). The IPOP relation of LP is, by BT, (26.2) x ( t ) [ LP ] y ( t ) = - sin ( t- ) ( t- ) x ( ) d , t R (i) Show that all -Band-Limited signals x ( t ) , that is, X ( i ) := F{ x ( t ) } = 0 , / [- , ] applied to LP will reappear as is at the OP terminal of LP . In other words the....
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This note was uploaded on 04/01/2008 for the course EE 102 taught by Professor Levan during the Spring '08 term at UCLA.

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102_1_Week-10-Recap - 48 NHAN LEVAN WEEK 10 RECAP 4 P13....

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