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fall 2003 EE 3120 final exam

# fall 2003 EE 3120 final exam - Name EE 3120 Final Exam SSN...

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Name:_____________________________________     EE 3120         Final Exam SSN:_______________________________________ Fall 2003 For the following difference equation: Answer questions 1-4 y[k] + 0.7y[k-1] + 0.1y[k-2] = u[k] + u[k-1] – u[k-2] 1. Find the z-transform with the initial conditions y[-1], y[-2]. Write the total  response in terms of the zero state and zero input responses.    2. What is the transfer function? 3. Plot the modes of the system.  Describe the behavior from these poles.

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4. If the input to the system is the unit step, and all initial conditions are all zero,  find the output y[k]. 5. Write the difference equation for the digital system with the following signal  flow graph:
6. Sketch the function  0.01 1 ( ) 2 t f t e - = .  What time can we consider to be infinite  for this function? 7. Find the largest sampling period of  sin 10 so that the frequency of its sampled  sequence equals the frequency of  sin 10 t .

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