Signal Notation

$x \in {\bf C}^N$ means is a length complex sequence
$x = x(\cdot)$
$X = \hbox{\sc DFT}(x) \in {\bf C}^N$
$X(k) = \hbox{\sc DFT}_k(x)$
$X(k) = \hbox{\sc DFT}_{N,k}(x)$ denotes the th bin of a length DFT
$X(k) \in {\bf C}$
$x(n) = \hbox{\sc IDFT}_n(X)$
$x(n)\in{\bf R}$ or ${\bf C}$
$n,k \in {\bf Z}$ or $n,k \in {\bf Z}_N$ (integers modulo )
For $x\in {\bf C}^\infty$ , $X = \hbox{\sc DTFT}(x) \in {\bf C}_{2\pi}^{\infty}$
$\overline{x} =$ conjugate of
$\angle x =$ phase of