2008.midterm1.solutions.ver3 - ECE 2704: MIDTERM EXAM 1...

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Unformatted text preview: ECE 2704: MIDTERM EXAM 1 Name: _______________________________SOLUTION_____________________ Signature:__________________________________________________________ NOTES: 1. One handwritten 8.5x11 sheet of paper is permitted. It must be your own handwriting. Electronic printing and photocopying is strictly prohibited. 2. Scores are based on correctness and clarity of presentation. 3. No calculators are allowed. 4. Put a box around your answers. 1. Compute the magnitude and phase (angle) of the following complex numbers a. Solution b. Solution , , 2. Suppose the impulse response of a linear timeinvariant system is . Is the system causal?. Hint: let be an arbitrary input and compute the corresponding output. SOLUTIONS The output is . Thus the system is causal. 3. Express in terms of . Your answer may have more than one term in it, but it should have no terms in it except those composed of simple transformations of . 4 3 2 1 2 Solution 4 3 2 1 4 6 2 4 6 The second term on the righthand side is found by timereversal, timeshift of to the right, . , followed by a 4. The impulse response of a system is Solution . Compute the output of the system to a unitstep. For , . For , 5. The stepresponse of a system is the output of the system when the input is a unit step . Suppose the step response of a linear timeinvariant system is . What is the output of the system when the input is the signal shown in Figure 1. 2 5 7 Figure 1: Input pulse . The signal in Figure 2 can be expressed . Since the system is linear and timeinvariant, the output is Solution When the input is , the output is ...
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