Consider the discrete-time signal x[n] shown below, where x[n] = 0 for n 3. 2 0 -1 -2 -6 -5 -3 - 1 1 5 6 0 Timen (a) In this part, you'll be comparing the DTFT that you calculated and the DFT calculated using MATLAB. i. Use MATLAB to plot the magnitude and phase of the DTFT of x[n] that you calculated in Part (a) as functions of angular frequency N. (6 points) ii. Next, create a MATLAB vector of length 1024 that starts with the nonzero values of x[n] and is otherwise 0. (This is called zero-padding and is often done when working with short signals. In this case, you're just adding values of x [n] at times n when x[n] = 0.) Use the MATLAB function fft to calculate the DFT of this signal and plot the magnitude and phase of the DFT as functions of angular frequency 12. (10 points) iii. How do the magnitudes and phases of the DTFT and the DFT compare to each other? If they are different, use the properties of the DTFT or the properties of the DFT to explain why. (5 points) Consider the discrete-time signal x[n] shown below, where x[n] = 0 for n 3. 2 0 -1 -2 -6 -5 -3 - 1 1 5 6 0 Timen (a) In this part, you'll be comparing the DTFT that you calculated and the DFT calculated using MATLAB. i. Use MATLAB to plot the magnitude and phase of the DTFT of x[n] that you calculated in Part (a) as functions of angular frequency N. (6 points) ii. Next, create a MATLAB vector of length 1024 that starts with the nonzero values of x[n] and is otherwise 0. (This is called zero-padding and is often done when working with short signals. In this case, you're just adding values of x [n] at times n when x[n] = 0.) Use the MATLAB function fft to calculate the DFT of this signal and plot the magnitude and phase of the DFT as functions of angular frequency 12. (10 points) iii. How do the magnitudes and phases of the DTFT and the DFT compare to each other? If they are different, use the properties of the DTFT or the properties of the DFT to explain why. (5 points)