Signal Notation

  • $ x \in {\bf C}^N $ means $ x$ is a length $ N$ 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 $ k$th bin of a length $ N$ 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 $ N$)
  • For $ x\in {\bf C}^\infty$, $ X = \hbox{\sc DTFT}(x) \in {\bf C}_{2\pi}^{\infty}$
  • $ \overline{x} = $ conjugate of $ x$
  • $ \angle x = $ phase of $ x$


Next Section:
Fourier Transform Notation
Previous Section:
Frequency and Time