1) Determine the autocorrelation function RXX(T) for the continuous-time random process X(t) that has the power spectrum (show all steps for your derivation)
where K > 0 is a real constant and WX is the spectral extent of the process.
2) Write a Matlab code to produce the estimated power spectrum from the autocorrelation function obtained in step (1) for N=5 normalized frequencies. Note: You may use the FFT function to calculate the Fourier transform. See Example 7.5-5
3) Plot on the same figure the estimated power spectrum on top of the given power spectrum
4) Repeat steps (2) and (3) for N=10 normalized frequencies.
5) Plot on the same figure the estimated power spectrum of step (4) on top of the given power spectrum
6) Compare your results