2-D Signals

We represent a 2-D signal as $x(n_1,n_2)$ where $x$ may be real-valued or complex-valued, and $n_1$ and $n_2$ are integer indices. We'll use $n_1$ as the horizontal index, and $n_2$ as the vertical index.

In image processing, the roles of $n_1$ and $n_2$ are interchanged in that $n_1$ is the row index and $n_2$ is the column index.

Figure 1: 2-D grid

• Examples
  • Sampled B/W photograph: $x(n_1,n_2)$

  • Sampled B/W video signal: $x(n_1,n_2,n_3)$ where $n_1$ and $n_2$ are the row and column indices of each frame and $n_3$ is the time index.

  • Sampled color video signal:
    Three fundamental standards are:
    • RGB (red, green, blue): Monitors
    • CMYK (cyan, magenta, yellow, black): Printers
    • YUV (luminance, chrominance): Broadcast TV

    An RGB video signal can be represented as:
    

    $$\left\{ \begin{array}{c} x_R(n_1,n_2,n_3)\\ x_G(n_1,n_2,n_3)\\ x_B(n_1,n_2,n_3)\\ \end{array} \right\}$$
    
    

  • Seismic array: $x(n_1,n_2)$