1. Write a short Matlab script or function (m-file) that generates the functions r(t) = e-atu(t)...

 

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1. Write a short Matlab script or function (m-file) that generates the functions r(t) = e-atu(t) for a = .1, 1, 10. Plot all functions in the same plot and use proper legends and label for your plot. 2. Using the definition of the FT (1), calculate the FT of the given functions in previous exercise. X (w) = x(t)e-jut dt (1) 3. Plot the absolute values and phase for the FT of the given three functions. One plot should contains the absolute value and the other the phase of them. Use proper legends to distinguish between function. Write a comment about the results for different value of a > 0. 4. Now just consider a = 1. Find the Fourier transfrom of r(t-5). Then plot the absolute value and phase of the signal in frequency domain. Compare the absolute value and phase of the Fourier transform of the shifted signal z(t - 5) and the absolute value and phase of the Fourier transform of the original signal r(t). 5. EXTRA CREDIT: You may have refered to a transform table to find the Fourier Transforms of your X(t). For extra credit have MATLAB calculate the integral and plot the frequency and phase plots. 1. Write a short Matlab script or function (m-file) that generates the functions r(t) = e-atu(t) for a = .1, 1, 10. Plot all functions in the same plot and use proper legends and label for your plot. 2. Using the definition of the FT (1), calculate the FT of the given functions in previous exercise. X (w) = x(t)e-jut dt (1) 3. Plot the absolute values and phase for the FT of the given three functions. One plot should contains the absolute value and the other the phase of them. Use proper legends to distinguish between function. Write a comment about the results for different value of a > 0. 4. Now just consider a = 1. Find the Fourier transfrom of r(t-5). Then plot the absolute value and phase of the signal in frequency domain. Compare the absolute value and phase of the Fourier transform of the shifted signal z(t - 5) and the absolute value and phase of the Fourier transform of the original signal r(t). 5. EXTRA CREDIT: You may have refered to a transform table to find the Fourier Transforms of your X(t). For extra credit have MATLAB calculate the integral and plot the frequency and phase plots.