soln2 - ECE320 Solution Notes 2 Cornell University Spring...

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ECE320 Solution Notes 2 Spring 2006 Cornell University T.L.Fine Please hand in this assignment at the end of lecture on Tuesday, 14 February. Use only your assigned three-digit code and not your name. 1. Consider the PAM signal s for a Gaussian pulse shape p ( t ) = e - αt 2 , s ( t ) = k = -∞ A k p ( t - kT ) . The role of the parameter α > 0 is that as it increases it makes the pulse narrower and effectively confined to a shorter time interval. By decreasing α we can simulate the effects of dispersion (broadening of the pulses) and of increasing the pulse repetition rate 1 /T (pulses closer together). Let the only n non-zero values A 0 , . . . , A n - 1 of { A k } be given by the Matlab command randn(1,n) for n = 10. (a) Use Matlab to plot (use subplot ) the three PAM signals s , corresponding to the same randomly chosen values of the information-bearing amplitudes { A k } , but for the three different α values of 0 . 3 , 1 . 0 , 3 . 0. See Figure 1. 0 1 2 3 4 5 6 7 8 9 10 -4 -2 0 2 Time PAM Signal 0 1 2 3 4 5 6 7 8 9 10 -4 -2 0 2 Time PAM Signal 0 1 2 3 4 5 6 7 8 9 10 -4 -2 0 2 Time PAM Signal Figure 1: PAM Signal (b) Estimate the true amplitudes { A k }

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• Spring '06
• FINE
• Probability theory, PAM signal, Poisson PMF

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