(Solved): 5. Consider the periodic discrete-time signal \( x[n] \) shown below. (a) Calculate the DTFS coeff ...

5. Consider the periodic discrete-time signal \( x[n] \) shown below. (a) Calculate the DTFS coefficients of \( x[n] \) by hand and plot them using MATLAB or python. If they're complex-valued, plot the real and imaginary parts and the magnitude and phase. Include your MATLAB or python code in your answer. (16 points) (b) Use MATLAB or python to show that the Fourier series representation of \( x[n] \) has the expected values for one period of \( x[n] \). Include your MATLAB or python code in your answer. (14 points)