What is the Fourier Transform of a constant signal?
I'll complete a bit the answer given in a comment above.

Intuitively first, to which frequency corresponds a signal constant in time, for exemple $x(t) = 1$ $\forall t$ ? Such a signal shows no variation in time and hence contains only a component with frequency 0 (this is a DC signal). This means that its  Fourier transform must be 0 everywhere, except in $f=0$. Mathematically, 
$$X(f) = \delta(f).$$
Now, can we prove this? Yes, simply take the inverse Fourier transform of $\delta(f)$ and use the properties of the Dirac delta $\delta(f)$
$$x(t) = \int_{-\infty}^\infty \delta(f)e^{j2\pi ft} \mathrm{d}f = \int_{-\infty}^\infty \delta(f) \mathrm{d}f = 1.$$