Notation and Terminology

If $X$ is the DFT of $x$, we say that $x$ and $X$ form a transform pair and write

$$\zbox {x\leftrightarrow X}$$   $$\mbox{(\lq\lq $x$\ corresponds to $X$'')}$$$$.$$

Another notation we'll use is

$$\begin{eqnarray*} \mbox{\sc DFT}(x)&\isdef & X,\quad\mbox{and} \\ \mbox{\sc DFT}_k(x)&\isdef & X(k). \end{eqnarray*}$$

As we've already seen, time-domain signals are consistently denoted using lowercase symbols such as ``$x(n)$,'' while frequency-domain signals (spectra), are denoted in uppercase (`` $X(\omega_k)$'').