Let \(x\left( t \right) = rect\left( {t - \frac{1}{2}} \right)\) where rect(t) = 1 for \( - \frac{1}{2} \le t \le \frac{1}{2}\) and zero otherwise, then Fourier Transform of x(t) + x(-t) will be given by

• A. \(\sin c\left( {\frac{\omega }{2}} \right)\)
• B. \(2\sin c\left( {\frac{\omega }{2}} \right)\)
• C. \(2\sin c\left( {\frac{\omega }{2}} \right)\cos \left( {\frac{\omega }{2}} \right)\)
• D. \(2\sin c\left( {\frac{\omega }{2}} \right)\sin \left( {\frac{\omega }{2}} \right)\)