Definition
A discrete signal is characterised by a series of samples spaced apart by a period Te. We apply the Fourier transform to a discrete signal x(n) as follows :
\(x\left(n\right)\rightarrow X\left(e^{j\omega}\right)=\sum_{n=-\infty}^{\infty}{x\left(n\right)e^{-j\omega n}=\sum_{n=-\infty}^{\infty}{x\left(n\right)e^{-j2\pi fn}=\sum_{n=-\infty}^{\infty}{x\left(n\right)e^{-j2\pi\frac{nf}{F_e}}}}}\) (1)
f and ω are two continuous variables; therefore, the Fourier transform (TF) of a discrete function results in a continuous function.