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ece 313 hw 7 - ECE 313 Fall 2010 Homework 7 –...

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Unformatted text preview: ECE 313 Fall 2010 Homework 7 – Due Thursday, October 28 (All book problems are from Chapter 6  copies of the problems from the book are attached.) 1. Problem 18, part a, p. 194. (Hint: Use a double ­integrated version of the equation.) 2. Problem 20, p. 194. 3. Problem 22, parts a, b, c, g, h, p. 195. (Hint: First determine how a general signal x ( t ) is affected by convolution with the scaled and shifted impulse Aδ ( t − T0 ) . Then you can solve all of the parts of this problem without having to evaluate additional convolution integrals. Also note that δT ( t ) = € example, δ 2 ( t ) = ∞ ∑δ ( t − nT ) – so for n =€ −∞ ∞ ∑δ ( t − 2n ) .) n = −∞ € Consider a CT LTI system having impulse response h ( t ) = t [ u( t ) − u( t − 1)] . Use 4. convolution to find the response y ( t ) to each of the following input signals. € Graph h ( t ) , and for each part, graph x ( t ) and y ( t ) . € € € (a) x ( t ) = δ ( t ) € (b) x ( t ) = 4 δ ( t − 2) € (c) x ( t ) = u( t ) (d) x ( t ) = 2[ u( t ) − u( t − 2)] € € (e) x ( t ) = 2[ u( t ) − u( t − 4 )] € 5. € For the system in Figure E.27, part b, p. 196: Find the input ­output differential equation and transfer function of the system, and find the system output if the € input is x ( t ) = cos( t ) . 6. 7. Problem 29, p. 196. (Graph the magnitude and phase of the transfer function evaluated at s = − j 2 π f as functions of f .) € Problem 32, part a, p. 197. € € ...
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