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(Solved): 4.1. Use the Fourier transform analysis equation (4.9) to calculate the Fourier transforms of: (a) ...


4.1. Use the Fourier transform analysis equation (4.9) to calculate the Fourier transforms of: (a) \( e^{-2(t-1)} u(t-1) \) (

4.1. Use the Fourier transform analysis equation (4.9) to calculate the Fourier transforms of: (a) (b) Sketch and label the magnitude of each Fourier transform.


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(a) To find the Fourier transform of    we can use the time-shifting property of the Fourier transform, which states that if f(t) has Fourier transform F(w), then    has Fourier transform F(w-a).

First, we can rewrite    as   , and then apply the time-shifting property with a=2:

F(w) = Fourier transform of   
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