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1 EE2353: Continuous-Time Signals and Systems: HOMEWORK #3 Fall 2015 , SOLUTIONS HOMEWORK PROBLEMS: (show your work and/or justify answers obtained by inspection) 3.1 a) items (ii) and (vi) (not (iv), it was a misunderstanding) Solution: Notice for very simple cases you can bypass the graphical approach and determine the limits directly from the step functions involved. In (vi) the u(t-) is not shown but u(t)u(t-) is non-zero only in the range [0,t] as in (ii). 3.2 g) Figures P3.2 below Solution: Keep h(t) fixed and flip and shift x(t) (uses the commutative property) 2 and Problem 3-A: A continuous-time LTI has the input x(t) and impulse response h(t), as shown below. a) Find the requested values of the output y(t) by inspection so there is no need to find equations for y(t). ANSWER: Give only these values of y(t) (Table below) b) Now obtain the complete signal y(t) and plot it (by hand). Details not shown but we can read off the form of y(t) from the graphical solution below as shown in class Solution: ANSWER: Give only these values of y(t) t -1 0 1 2 3 4 5 6 y(t) 0 0 0 t-1=0 -4 t-1=1 0 t-1=2 4 t-3=1 0 t-3=2 0 3.8 Modified as shown below Solution: The first one is actually part b) in Problem 3.8 (5th edition book) h(t)x(t) t-3 t-1 h(t-) 2 x() 4 -4 y(t) 54);5(4 42);3(4 21);1(4 5;1;0 )( tt tt tt tt ty 3 The second one is here
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