$ - x(f) = F.T[x(t)]$ $= \int_\infty^\infty x(t) e^{-jwt dt.}$ 1] Unit step: ASSUMPTION : Unit step is converging function. $\therefore$ x(t) = 1 t $\geq$ 0 = 0 t \lt 0 $\therefore$ x(f) $= \int_0^\infty l. e^{-jwt dt.}$ $= [ \frac{e^{-jwt}}{-jw}]_0^\infty$ $= 0 - \frac{1}{{-jw}}$ $x(f) = \frac{1}{jw}$ 2] Delta function: x(t) = 1 t = 0 = 0 t $\neq$ 0 $\therefore$ x(f) $= \int_t=0 l.e^{-jwt dt.}$ x(f) = $e^{-jst/_t}=0$ x(f) = 1 3] Gate function: x(t) = A $\frac{-z}{2} < t < + z/2$ = 0 else where. $\therefore$ x(f) $= \int^{z/2_z/2 A.} e^{-jwt dt.}$ $= \frac{A}{-jw} [ e^{-jwt]^{z/2}}$ $= \frac{A}{jw} [ e^{jwz/2} \ - \ e^{-jwz/2]}$ $x(f) = \frac{2A}{jw} \ sin \ (w\frac{z}{2})$