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First imagine what looks like. It consists of a rectangle centered at of width, 2, multiplied by a complex exponential. Therefore for frequencies greater than one in magnitude it is zero. Its magnitude is simply the magnitude of the rectangle function because the magnitude of the complex exponential is one for any f.
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The phase (angle) of is simply the phase of the complex exponential between and and undefined outside that range because the phase of the rectangle function is zero between and and undefined outside that range and the phase of a product is the sum of the phases. The phase of the complex exponential is
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The inverse tangent function is multiple-valued. Therefore there are multiple correct answers for this phase. The simplest of them is found by choosing
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which is simply the coefficient of j in the original complex exponential expression.
A more general solution would be . The solution of the original problem is simply this solution except shifted up and down by 10 in f and added.
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