Write a MATLAB program that generates and graphs the noisy cosine sample paths Xcc(t), Xdc(t), Xcd(t), and Xdd(t) of Figure 13.3. Note that the mathematical definition of Xcc(t) is
Xcc(t) = 2cos(2πt) + N(t), -1 < t < 1.
Note that N(t) is a white noise process with autocorrelation RN(τ) = 0.01δ(τ). Practically, the graph of Xcc(t) in Figure 13.3 is a sampled version Xcc[n] = Xcc(nTs), where the sampling period is Ts = 0.001s. In addition, the discrete-time functions are obtained by sub-sampling Xcc[n]. In sub-sampling, we generate Xdc[n] by extracting every kth sample of Xcc[n]; see Problem 13.8.5. In terms of MATLAB, which starts indexing a vector x with first element x(1),
Xdc(n) = Xcc(1 + (n-1)k).
The discrete-time graphs of Figure 13.3 used k = 100.