Consider the function () = ( + ) ( ) where u(t) is the "unit step function" defined as:

u(t) = 0 for t<0 u(t) = 1 for t>0

and a>0 .

i) Sketch a graph of u(t) versus t ii) Sketch graphs of u(t+a) versus t and u(t-a) versus t iii) Sketch a graph of x(t) versus t

iv) For the function x(t), starting with the definition of a Fourier Transform, evaluate the integral and simplify in order to derive the Fourier Transform of the function x(t).