spring04_pset14

# spring04_pset14 - t 3 Find the bandwidth of the signal Δ...

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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.

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Unifed 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 book.
Unifed Engineering II Spring 2004 Problem S20 (Signals and Systems) Do problem 7.26 in Oppenheim and Willsky.

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Unifed 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, Δ
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Unformatted text preview: t . 3. Find the bandwidth of the signal, Δ ω . You may want to use the time domain formula for the bandwidth. 4. How close is the answer to the theoretical lower bound? Explain why the answer is or is not close to the bound. ± ² ± ² Unifed Engineering II Spring 2004 Problem S2 2 (Signals and Systems) Consider a pulse similar to the Loran-C pulse, given by 3 h ( t ) = t e − t/τ σ ( t ) sin(2 πft ) = g ( t ) w ( t ) where te − t/τ σ ( t ) g ( t ) = w ( t ) = sin(2 πft ) (a) Find the centroid of the pulse envelope, given by ¯ tg 2 ( t ) dt t = g 2 ( t ) dt (b) Find the duration of the envelope, given by ¯ ( t − t ) 2 g 2 ( t ) dt Δ t = 2 g 2 ( t ) dt (c) 1 2 g ˙ 2 ( t ) dt Δ ω = 2 g 2 ( t ) dt 1 2 (d) How does the duration-bandwidth product compare to the theoretical minimum?...
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spring04_pset14 - t 3 Find the bandwidth of the signal Δ...

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