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ECE111_2008SPRING_EXAM1__[0]

ECE111_2008SPRING_EXAM1__[0] - The Cooper Union Department...

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The Cooper Union Department of Electrical Engineering ECEIII Signal Processing & Systems Analysis Exam I March 7, 2008 Time: 2 hows. Closed book., closed notes. No calculators. 1. [8 pts.] Starting from the general fonnula for the DTFI', determine the Fourier transform of (no ~ n) in terms of the Fourier transform X (w) of x (n). Note that 7l{l is a constant. Also, do not simply invoke some properties you may remember; you have to DEIUVE an expression from the DTIT formula. 2. [3 pts.) Write the IDTFI' formula. 3. [6 pts.] The spectrum X (w) for a discrete-time signal is shown in Figure P3. (a) Extend the axes to the range - 211" to 211". (h) \[ Y (w) ~ X (2w), sketch I' (w) ov., lhe "nge -21< to 2 •. 4. [10 pts.j A digital filter is given by: y(n) ~ 2x(n) -3x(n -1) + 4x(n - 2) Specify the impulse response, transfer function and frequency response of the filter. Sketch a. transversal filter realization. - 5. [5 pts.J Waveforms x (t) and It (t) are shown in Figure P5. Let y = h * x. Do noL compute y (t) for all t! Just do the following: (a) Use the flip and slide method (draw a sketch) to compute y (l). (b) Specify the support of y. 6. [3 pts.] Sketch lhe waveronn 2u (t - 1) + 3u (2 - t) + u (2t). 7. [4 pts.] Let h, x be discrete-time signals such that h has nOD-zero values at even times only, and x has non-zero values at odd times only. Is that enough information to determine whether y = h * x has nonzero values only for even times, or only for odd times? Justify BRlEFLY.

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ECE111_2008SPRING_EXAM1__[0] - The Cooper Union Department...

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