20115ee102_1_hw6

20115ee102_1_hw6 - H s 2(b We would like to design a system...

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1 EE102 Systems and Signals Fall Quarter 2011 Jin Hyung Lee Homework #6 Due: Wednesday, Nov. 23, 2011 at 5pm 1. Response of compound systems H 1 (jω) H 2 (jω) G 1 (jω) G 2 (jω) F 1 (jω) F 2 (jω) + - - + - + + + α 1 α 2 x(t) y(t) Derive the overall system response H ( ) in frequency domain. Express it in terms of α 1 , α 2 , H 1 ( ) , H 2 ( ) , G 1 ( ) , G 2 ( ) , F 1 ( ) , and F 2 ( ) . 2. Multipath Cancellation A common problem in communications, radar, and sonar is multipath . This occurs when there are multiple paths from a transmitter to a receiver, each with a different path length and propagation delay. The results is that the receiver gets multiple interfering copies of the message. Direct Path Reflected Path Transmitter Receiver We can model the simple case of two paths as a system with the impulse response h ( t ) = δ ( t ) + ( t - T ) where T is the difference between the propagation delays along the two paths. (a) Find the transfer function of this system
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Unformatted text preview: H ( s ) 2 (b) We would like to design a system H c ( s ) that takes the received signal y ( t ) and cancels the multipath component, so that the output signal r ( t ) is the same as x ( t ) . H ( s ) H c ( s ) x ( t ) y ( t ) r ( t ) What is transfer function of of the canceller system H c ( s ) ? (c) Find the impulse response of canceller ( Hint: 1 1-x = 1 + x + x 2 + x 3 ··· for | x | < 1 ). 3. Inverse Laplace Transforms Find the Inverse Laplace transforms of the following functions (suppose the system is ra-tional and causal) (a) s ( s + 1)( s-1) (b) s + 3 ( s + 1)( s + 2) 4. Find the impulse response h ( t ) for the following Causal and Rational system. 3-6 3-5-6 1/S 1/S x(t) y(t)...
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20115ee102_1_hw6 - H s 2(b We would like to design a system...

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