Be sure to include the MATLAB simulations. Simulate for a = 1 and a = 8. If the answer does not include a MATLAB simulation with the code, it will be incomplete.

Problem 1. Fourier Transform of a Rectangular Pulse Consider the signal of Figure 1: X(t) t -a Figure 1: Rectangular pulse signal a) 20 points: Find the Fourier Transform, in magnitude and phase. b) 30 points: (i) Sketch by hand the Spectral Density for a large and for a small. Explain in words the meaning of the Spectral Density in both cases. (ii) Create a MATLAB simulation experiment to verify your analysis. Problem 1. Fourier Transform of a Rectangular Pulse Consider the signal of Figure 1: X(t) t -a Figure 1: Rectangular pulse signal a) 20 points: Find the Fourier Transform, in magnitude and phase. b) 30 points: (i) Sketch by hand the Spectral Density for a large and for a small. Explain in words the meaning of the Spectral Density in both cases. (ii) Create a MATLAB simulation experiment to verify your analysis