1 determine the autocorrelation function rxxt for the

Question

1) Determine the autocorrelation function R_XX(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

Answer 1

For the following diagram, consider the information and give answers to the following questions. 1) Find out the autocorrelation function RXX(T) for the continuous-time random process X(t) that consist of the power spectrum (illustrate all steps for your derivation) In which, K > 0 is a real constant and WX is the spectral extent of the procedure. 2) Write down a Matlab code to produce the estimated power spectrum from the autocorrelation function obtained in step (1) for N=5 normalized frequencies. 3) Plot on the similar figure the estimated power spectrum on top of the provided power spectrum. 4) Repeat the steps (2) and (3) for N=10 normalized frequencies. 5) Plot on the similar figure the estimated power spectrum of step (4) on top of the particular power spectrum. 6) Compare your outcomes.