ECE111_2007SPRING_EXAM1__[0] - The Cooper Union Department...

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The Cooper Union Department of Electrical Engineering ECElll Signal Processing Systems Analysis Exam I March 2, 2007 Time: 2 ours. Closed book, closed notes. No calcuJators. I. 12 prs,} What do FIR and fIR stand for? (Not the defioitioos) 2. [8 pts.] A digital filter is given hy, y (n) = 3x (n) ~ 2x (n - 1) + 5x (n - 2) + fix (n - 3) S ify the impulse response, transfer function and frequency response of the filter. SketCh a transversal filter realization. Is t.he filter FIR or HR.? ~. [5 P'llts. J Determine the transfer function for the block diagram shown in Figure 3. You do not need to simplify the expression. 4. [10 pts.J A 10M H z signal is sampled at a rate f .. stored digitally, and played back at af rate 20NfHz, resulting in an output signal at 5MH z. Assume no aliasing or imafn g distortion occurs during the AID or D/A conversion. (a) IExpress the input signal frequency on the following scales: analog radian fre- I quency, digital radian frequency, fraction of sampling rate, fraction of Nyquist bandwidth. (b) 'Express the output signal frequency on the same scales as above. (c) What is the sampling rate of the AID? (d) List the first four frequencies (in Hertz) above lOMHz that would cause aliasing distortion at the AID converter input. (e) List the first four frequencies (in Hertz) flbove 5MHz that correspond to imaging distortion at the Dj A converter output, 5. [4 P s.} Let It (t) = e- n '" (t) and x (t) = e- P '" (t), where ex, f3 > o. Let Y = It * x. We are i terested in computing y (1), only! I (al Sketch It (tl and x (t). (b) Draw a sketch that would help you compute y (1) using the "flip and slide" graph- 'ical method. (c) IStarting with the general formula for the convolution integral (write the in- tegral!), set it up to compute y (1). Confirm that the integral fonnula you come up with "matches" the sketch, specifically, show that you need to com- I Pute y (1) = .C (blah)dt where the bounds of the integral match what you see in yOllr sketch.
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ECE111_2007SPRING_EXAM1__[0] - The Cooper Union Department...

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