s15_ps12_spring04

s15_ps12_spring04 - Unified Engineering II Spring 2004...

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Unformatted text preview: Unified Engineering II Spring 2004 Problem S15 (Signals and Systems) Find the Fourier transforms of the following signals: 1. g (t) = δ (t − T ) Note: The system with impulse response g (t) produces an output that is the input delayed by T . Since delays occur frequently in signal processing, G(jω ) is an important transfer function. 2. � 1, |t| ≤ T g (t) = 0, |t| > T Note: Because g (t) is symmetric, G(jω ) should be real. Please express your answer so that it is apparent that the answer is real. 3. 1 + T2 Hint: If you find the integral hard to do, you might be able to find the answer using duality. g (t) = 4. g (t) = t2 sin π t/T π t/T Hint: You almost certainly won’t be able to do the FT integral directly. Use duality and the results of (2) above to find the answer. The g (t) in this problem has important connections to, among other things, CD players! 5. Find the inverse transform of � G(jω ) = sin ω T ωT �2 using the results of part (2), and FT properties. ...
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