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HW3.2008.SOLUTIONS - ECE 2704 Homework Number 3 Due at the...

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Unformatted text preview: ECE 2704 Homework Number 3 Due at the start of class on Wednesday, 6 February 2008 1. Exercise 1.44 (a), (b), (c), (d), (g) Solutions (a) From our definition of the Dirac delta, (b) Perform a change of variables were , then (c) (d) (g) Perform a change of variables with , 2. Suppose Solution . Compute 3. Exercise 1.46 (no need to sketch the result, just express the result as a function) There is a typo in the problem statement. It should read Solution Let the function shown by expressed as that , . . Recall Thus Note that we can also express the result as 4. Exercise 1.51(b) (c) Solution (a) The even part is 2 . 1 0 The odd part is 2 1 0 0 1 2 . Thus (b) Note that 5. Exercise 1.71 (a) (b) (h) Solutions (a) Consider the input/output pairs Let and and is odd and the even component is zero. and that satisfy be scalar constants. To assess linearity, we seek to determine if is also a input output pair. Note that Thus the system is NOT linear. (b) Consider the input/output pairs and Note that and that satisfy Thus the system is linear. (h) Thus the system is linear. 6. Exercise 1.710 . Ignore the questions and simply write the simplest possible expression for in terms of signals. Solution This is the odd part of the of the signal . and then explain what this system does in terms of even and odd parts of ...
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