Notation and Terminology

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

$$\zbox {x\;\longleftrightarrow\;X}$$   $$\mbox{(\lq\lq $x$\ corresponds to $X$'')}$$$$. \protect$$

Another notation we'll use is

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

If we need to indicate the length of the DFT explicitly, we will write $\hbox{\sc DFT}_N(x) = X$ and $\hbox{\sc DFT}_{N,k}(x) = X(k)$. 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 (`` $X(\omega_k)$'').