N261H3 - (w), 1/2 (t), -1/5 (t 1), 1/(2-j3) (w + 3), k (w)...

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EGR 261 Due date: ______________________ Signals and Systems (See Due Dates Table) File: N261H3 Homework Assignment #3 Reading Assignment : Ch. 1, Sect. 1-4, 6-8 in nd Ed . by Lathi Problem Assignment : Work the following problems from Chapter 1 in nd Ed . by Lathi: 1.1-1, 1.1-2, 1.1-5, 1.1-6 (See note on problem 1.1-1 below) 1.2-2, 1.2-3 (find x 1 (t) and x 2 (t) only) 1.4-1, 1.4-2, 1.4-3, 1.4-4 1.7-1, 1.7-7, 1.7-8, 1.7-11 1.8-1, 1.8-2 Problem 1.1-1) The waveforms in the text left off the time values on the t axis. They are shown below. Selected Answers : 1.1-1 3, 3, 3, 12 1.1-2 1/3, 1/3, 1/3, 1/3, 4/3 1.1-5 75, 178, 51, 25, 25, 1/2 1.1-6 P x = A 2 /6, E x = 1.2-3 x 1 (t) = x(t + 1) + x(1 – t), x 2 (t) = x([t + 1]/2) + x([1 – t]/2) 1.4-2 x 1 (t) = (4t + 1)[u(t + 1) – u(t)] + (-2t + 4)[u(t) – u(t – 2)] x 2 (t) = t 2 [u(t) – u(t – 2)] + (2t – 8)[u(t – 2) – u(t – 4)] 1.4-3 0, 2/9
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Unformatted text preview: (w), 1/2 (t), -1/5 (t 1), 1/(2-j3) (w + 3), k (w) 1.4-4 x(t), x(t), 1, 0, e 3 , 5, x(-1), -e 2 1.7-1 Only b, f, and h are linear. Use the procedure discussed in Example 1.9 for each part. 1.7-7 Only part a is causal. Explain why in each case! 1.7-8 a) Invertible. Inverse system equation is y(t) = dx/dt. b) Non-invertible. Why? c) Non-invertible. Why? d) Invertible (but noncausal). Inverse system equation is y(t) = x(t/3 + 3) e) Non-invertible. Why? f) Invertible. x(t) = ln[y(t)] Page 2 1.7-11 No, Yes, No, Yes, Yes (explain why in each case) 1.8-1 1.8-2 Dx(t) (t) 3)y (D or x(t) dt d (t) 3y (t) y dt d x(t) (t) 3)y (D or x(t) (t) 3y (t) y dt d 2 2 2 1 1 1 = + = + = + = + Dx(t) (t) 2)y 2D (D or x(t) dt d (t) 2y (t) y dt d 2 (t) y dt d x(t) D (t) 2)y 2D (D or x(t) dt d (t) 2y (t) y dt d 2 (t) y dt d 2 2 2 2 2 2 2 2 1 2 2 2 1 1 1 2 2 = + + = + + = + + = + +...
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This note was uploaded on 02/11/2010 for the course EGR 261 taught by Professor Staff during the Fall '09 term at Delaware State.

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N261H3 - (w), 1/2 (t), -1/5 (t 1), 1/(2-j3) (w + 3), k (w)...

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