Texts: A rectangular pulse, (t), of width T as shown overleaf in Figure B1, is defined by:
0, 2/L -> 7
A if -T/2 < t < T/2
0, t T/2
The Fourier transform of the signal, (t), is denoted by X(w) and expressed as:
X(w) = A7
(e
A signal, y(t), is described by the equation:
if to - T/2 < |t| < to + T/2 otherwise
where to > 0 is a positive constant, and t means the magnitude of t
(i)
Carefully plot the signal, y(t), paying attention to the region when y(t) is non-zero, and labeling all axes.
(ii)
Calculate the Fourier transform of the signal, y(t), denoted by Y(w).
Clearly show all your steps and working, but note that marks are awarded for concise approaches rather than a verbose long-winded solution.
(iii)
Provide an alternative derivation to calculate Y(w), different from your method in part (ii) and using further properties of the Fourier transform not already used.
(iv)
Simplify your answer for the case to = t/2, and explain how you can check if this solution is correct.
