ECE111_2006SPRING_EXAM3__[0]

ECE111_2006SPRING_EXAM3__[0] - The Cooper Union Department...

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Cooper Union Department of Electrical Engineering ECElll Signal Processing Systems Analysis Exam III May 1, 2006 Time: 90 min. Closed book, closed notes. No calculators. SHOW ALL WORK!! 1. [4 pts.] Write what each of the following abbreviations stand for (do not define the terms, simply write out the full words): (a) WSS (b) SSS (c) PSD (d) ARMA 2. [4 pts.] A block of 100 samples, x (n) for 1 ::; n ::; 100, of a WSS random signal are obtained. The signal is complex valued! (a) Write a formula that estimates the correlation value r (2) from the data. (b) The basic property that is being assumed here is (one word, does not begin with the letter s' ). 3. [5 pts.] Given the PSD Sx (w) of a discrete-time random signal. Write a general formula for the correlation r x (m) in terms of Sx (w). 4. [9 pts.] A random signal x (n) is such that the signal v (n) obtained as: v (n) = x (n) - O.lx (n - 1) + 0.2x (n - 2) is O-mean white noise with variance O"~ = 4. (a) Is x AR, MA or ARMA? (b) Write an explicit formula for the PSD of x as a function of w (not z); the formula must be explicit but does not have to be simplifud. (c) Is the above difference equation, with x as input and v as output, the whitening filter of x? If not, what is it called? (d) Write the difference equation for the inverse filter, with v as input and x as output. What is this filter called? (e) The white noise signal v is called the signal of x. 1
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ECE111_2006SPRING_EXAM3__[0] - The Cooper Union Department...

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