Consider the function x(t) defined as x(t)= 2 sin(at) for 0 St 1 and x(t) = 0 otherwise. (a) Argue that the bandwidth of this signal should be smaller than that of a rectangle of the same duration and use this fact to choose a suitable sampling frequency. (b) Plot the signal in the time domain using MATLAB. (c) Plot the Fourier transform using MATLAB. (d) Compare the absolute value of the Fourier transform with that of a rectangle of the same duration using MATLAB. Explain the differences