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20095ee102_1_EE102_ HW7

20095ee102_1_EE102_ HW7 - 0 1 0 kt e t a f t t t b f t t...

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EE102 HW 7 Fall 2009 1. Given the following formula for the Fourier Transform and the Inverse Fourier Transform: 2 2 ( ) ( ) ( ) ( ) j ft t j ft f F f f t e dt f t F f e df π - =-∞ =-∞ = = Find the Fourier Transform of the following functions: | | | | | | ) ( ) (1 | |) sin( ) ) ( ) ) ( ) ( ) t t t a f t e t t b f t e t c f t e t δ - - - = + = = 2. Find the Inverse Fourier Transform of the following functions: 2 2 2 sin( ) ) ( ) 1 ) ( ) 1 4 f a F f f b F f f = ÷ = + 3. What is the Fourier Transform of the following function:
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Unformatted text preview: , ) ( ) 0 , 1, ) ( ) 0 , kt e t a f t t t b f t t- ≥ = < ≥ = < What you would get for part b, if you consider f(t) as the integral of ( ) t ? 4. Show that the Fourier Transform of ( ) cos(2 ) f t f t = is [ ] 1 ( ) ( ) ( ) 2 F f f f f f =-+-...
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