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Signals, Systems & Information Problem Set 7 Solutions PS 73 (b) nun!Z X1 n=1 nunz n= X(z) X(z) = z 1 2z 2 3z 3 4z 4 z 1X(z) = z 2 2z 3 3z 4 (1 z 1)X(z) = 1 1 z 1 z 2 z 3 z 4 = 1 1 1 z 1 z 1 1 z 1 X(z) = z 1 (1 z 1)2 ROC jz 1j11 05 0 05 1105 0 05 1 Real part Imaginary part 2 One zero at z=¥ Figure 2 zplane plot for (b) xn = nun PS 73Y = a e^(b x) where a and b are constants The curve that we use to fit data sets is in this form so it is important to understand what happens when a and b are changed Recall that any number or variable when raised to the 0 power is 1 In this case if b or x is 0 then, e^0 = 1 So at the yintercept or x = 0, the function becomes y = a * 1 orThe answer is 0 Do you see why??
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