EE661 -Modulation TheorySpring 2011Practice Midterm Exam #1Problem 1.(25 points) Zero-mean, white Gaussian noise with a PSD of is passed through a BPF whose transfer function is as described in the figure. (a) Find the variance of the I and Q components of the output bandpass noise.(b) Are the I and Q components of the noise independent? Carefully justify your answer.Problem 2.(25 points)The four waveforms listed below are used to form a 4-ary signalling format., ,,, ,.(a) Find a set of orthonormal basis functions such that each waveform can be written as a linear combination of the set of basis functions.(b) Find the vector representation of each of the four signals and plot the signal space diagram. Be sure to label and scale your axes appropriately.(c) Suppose that the received signal is for . Convert this signal to a received vector and plot the vector on the signal space diagram from part (b). Which signal should the receiver decide in favor of?Problem 3.(25 points)A binary baseband pulse position modulation format,
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