Tutorial9_solution - 1 Tutorial 9 Principles of...

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Principles of Communications 1 Tutorial 9
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Principles of Communications 2 Problem 1 (Matched Filter) Consider the transmitted signal: 1) Draw the impulse response of the corresponding matched filter. 2) Draw the output of the matched filter with an input positive rectangular pulse of the form . 3) What is the output of the correlator? Compare it with the sampled output of the matched filter at t = τ . s ( t ) = s 1 ( t ) = 1, if b 1 = 1 s 2 ( t ) = 0, if b 1 = 0 0 t τ s 1 ( t )
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Principles of Communications 3 Solution 1) The impulse response of the matched filter is given by h ( t ) = s 1 ( τ t ), 0 t τ 0 τ 1 t 0 - τ 1 t 0 τ 1 t h ( t ) = s 1 ( τ t ) s 1 ( t ) s 1 ( t ) We have
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Principles of Communications 4 Solution 2) The output of the matched filter is given by z ( t ) = s 1 ( t ) h ( t ) = s 1 ( x ) h ( t x ) dx 0 t That is: * 0 τ 1 t 0 τ 1 t 0 τ τ 2 τ t s 1 ( t ) h ( t ) z ( t ) = 0, t < 0 1 dx 0 t = t , 0 t τ 1 t τ τ dx = 2 τ t , τ t 2 τ 0, t > 2 τ
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