Tuto7_sol - EE3210 Tutorial 7 (Solution) 1. (Problem 4.36...

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Unformatted text preview: EE3210 Tutorial 7 (Solution) 1. (Problem 4.36 in the Textbook) a) We first find the Fourier Transform of x(t) and y(t): ) 4 )( 1 ( 6 4 2 1 2 ) ( ) 3 )( 1 ( 2 4 3 1 1 1 ) ( ω ω ω ω ω ω ω ω ω ω ω j j j j j Y j j j j j j X + + = + − + = + + + = + + + = Then we can find the frequency response: ) 2 )( 4 ( ) 3 ( 3 ) ( ) ( ) ( ω ω ω ω ω ω j j j j X j Y j H + + + = = b) Expand the frequency response into partial fractions, we obtain: ω ω ω j j j H + + + = 2 2 / 3 4 2 / 3 ) ( Taking its inverse Fourier transform, we obtain [ ] ) ( 2 3 ) ( 2 4 t u e e t h t t − − + = c) We have 2 ) ( 6 8 3 9 ) 2 )( 4 ( ) 3 ( 3 ) ( ) ( ω ω ω ω ω ω ω ω j j j j j j j X j Y + + + = + + + = Cross-multiplying and taking the inverse Fourier transform, we have ) ( 9 ) ( 3 ) ( 8 ) ( 6 ) ( 2 2 t x dt t dx t y dt t dy dt t y d + = + + . 2. Since the two systems are cascaded, the frequency response of the overall system is ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + = ⎥ ⎥ ⎥ ⎥...
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Tuto7_sol - EE3210 Tutorial 7 (Solution) 1. (Problem 4.36...

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