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ECE 630: Statistical Communication Theory
Prof. B.-P. Paris
Homework 3
Due: February 16, 2017
where the frequency F is uniformly distributed over the interval [0,f_{0}].
Now suppose we redefine the process X_{t} to be
where F and Θ are statistically independent random variables. Θ is uniformly disributed over [-π,π) and F is distributed as before.
The output process is labeled Y _{t}. The mean of Y _{t} is measured to be and the covariance function of Y _{t} is found to be
Here H_{1}(f) is the transfer function of an ideal bandpass filter and H_{2}(f) is an ideal lowpass,
Assume that Δf is small compared to the range of frequencies over which S_{X}(f) varies, i.e., you may assume that S_{X}(f) is constant over intervals of width Δf.