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MIT 16 01 - Signals and Systems

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Massachusetts Institute of Technology Department of Aeronautics and Astronautics Cambridge, MA 02139 16.03/16.04 Unified Engineering III, IV Spring 2004 Problem Set 14 Name: Due Date: Not Due Time Spent (min) CP21-23 S19 S20 S21 S22 Study Time Announcements: Final on Wednesday, 5/19, 9am.Unified Engineering II Spring 2004 Problem S19 (Signals and Systems) Do problems 7.1–7.4 in Oppenheim and Willsky. Note: The solutions are in the back of the bo ok.Unified Engineering II Spring 2004 Problem S20 (Signals and Systems) Do problem 7.26 in Oppenheim and Willsky.Unified Engineering II Spring 2004 Problem S21 (Signals and Systems) Consider the signal g(t) = (1 + |t|)e−|t| 1. Plot the signal. Do you expect the signal to have a “good” duration-bandwidth product, meaning that the product is close to the lower bound? 2. Find the duration of the signal, Δt. 3. Find the bandwidth of the signal, Δω. You may want to use the time domain formula for the bandwidth. 4. How close is the answer to the theoretical lower b ound? Explain why the answer is or is not close to the bound.� �� ��� �Unified Engineering II Spring 2004 Problem S2 2 (Signals and Systems) Consider a pulse similar to the Loran-C pulse, given by 3h(t) = t e−t/τ σ(t) sin(2πf t) = g(t)w(t) where te−t/τ σ(t)g(t) = w(t) = sin(2πft) (a) Find the centroid of the pulse envelope, given by ¯tg2(t) dt t = � g2(t) dt (b) Find the duration of the envelope, given by ¯(t − t)2g2(t) dt Δt = 2 � g2(t) dt (c) 1 2 g˙2(t) dt Δω = 2 � g2(t) dt 1 2 (d) How does the duration-bandwidth product compare to the theoretical


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MIT 16 01 - Signals and Systems

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