For signals with infinite support, their Fourier transforms cannot be derived from the Laplace transform unless they are absolutely integrable or the region of convergence of the Laplace transform contains the j??-axis. Consider the signal x(t) = 2e^?2?t?

(a) Plot the signal x(t) for ??

(b) Use the evenness of the signal to find the integral

and determine whether this signal is absolutely integrable or not.

(c) Use the integral definition of the Fourier transform to find X(?).

(d) Use the Laplace transform of x(t) to verify the above found Fourier transform.

(e) Use MATLAB?s symbolic function fourierto compute the Fourier transform of x(t). Plot the magnitude spectrum corresponding to x(t).

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