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2. Determining the Sampling Frequency Consider the analog signal x(t) = u(t + 0.5) - u(t - 0.5). Mathematically derive the Fourier transform of x(t). Check your answer in MATLAB using the code. Make sure you understand these two lines of code by writing a paragraph explaining the code. syms t a = simplify(fourier((heaviside(t + 1/2) - heaviside(t - 1/2)))) Since x(t) is not bandlimited, the discussion in class explained how to find a suitable Î©max for x(t) so that the sampling theorem can be applied. Summarize this class discussion using mathematical equations. Consider the supplied MATLAB code lab1q2.m. Add comments to the code that show your understanding and submit the commented code as part of your lab report. Run lab1q2.m and suggest a useful sampling frequency for x(t) such that about 99% of the total energy of the signal is captured.

          2. Determining the Sampling Frequency
    
    Consider the analog signal x(t) = u(t + 0.5) - u(t - 0.5). Mathematically derive the Fourier transform of x(t). Check your answer in MATLAB using the code. Make sure you understand these two lines of code by writing a paragraph explaining the code.
    
    syms t
    a = simplify(fourier((heaviside(t + 1/2) - heaviside(t - 1/2))))
    
    Since x(t) is not bandlimited, the discussion in class explained how to find a suitable Î©max for x(t) so that the sampling theorem can be applied. Summarize this class discussion using mathematical equations.
    
    Consider the supplied MATLAB code lab1q2.m. Add comments to the code that show your understanding and submit the commented code as part of your lab report. Run lab1q2.m and suggest a useful sampling frequency for x(t) such that about 99% of the total energy of the signal is captured.

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