Write a Matlab code to produce the estimated power spectrum...1 answer below »

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) 2 ( ) cos rect 2 2 XX X X K W W p? ? ? ? ?? ? = ? ?? ? ? ?? ? L 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

Document Preview:

EE315_2
Name: ID:
• Submit a Hard and, including MATLAB codes.
• Print and use this cover page.
1) Determine the autocorrelation function R (t) for the continuous-time random
XX
process X(t) that has the power spectrum (show all steps for your derivation)
?? ??
p? ?
2
L () ? = Kcos rect
XX ?? ??
22 WW
??XX??
where
K > 0 is a real constant and W is the spectral extent of the process.
X
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
Points will be given for report format, correct program code, comparison, full clear
complete plots, use of the cover sheet and submission on time
Submit hardcopy of your work in the class on May 4 , 2013.

Solution: Given the continuous time random process X(t) that has a power spectrum as Where K>0 is a real constant and is the spectral extent of the process. The autocorrelation function is obtained by taking the inverse Fourier transform of the power spectral density clear N = 5; k = 1; Ts = 1; wx...

Solution Preview:

Solution: Given the continuous time random process X(t) that has a power spectrum as Where K>0 is a real constant and is the spectral extent of the process. The autocorrelation function is obtained by taking the inverse Fourier transform of the power spectral density clear N = 5; k = 1; Ts = 1; wx...