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Some 2D signals are <math>\ \delta\left (\mathit{x}, \mathit{y}\right )</math>,Rect<math>\left (\mathit{x}, \mathit{y}\right )</math>,Sinc<math>\left (\mathit{x}, \mathit{y}\right )</math>.One important property of 2D functions is that they are separable,when they are a product of two 1D signals.They are of the form : | Some 2D signals are <math>\ \delta\left (\mathit{x}, \mathit{y}\right )</math>,Rect<math>\left (\mathit{x}, \mathit{y}\right )</math>,Sinc<math>\left (\mathit{x}, \mathit{y}\right )</math>.One important property of 2D functions is that they are separable,when they are a product of two 1D signals.They are of the form : | ||
| − | <math>\ \mathbf{f}\left (\mathit{x}, \mathit{y}\right )=\mathbf{g}\left (\mathit{x}\right )\mathbf{h}\left (\mathit{y}\right) | + | <math>\ \mathbf{f}\left (\mathit{x}, \mathit{y}\right )=\mathbf{g}\left (\mathit{x}\right )\mathbf{h}\left (\mathit{y}\right)</math> |
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<math>Rect<math>\left (\mathit{x}, \mathit{y}\right ) = <math> | <math>Rect<math>\left (\mathit{x}, \mathit{y}\right ) = <math> | ||
| + | \begin{cases} | ||
| + | 1, & \mbox{if }|x|&|y|\mbox{ is less than 1} \\ | ||
| + | 0, & \mbox{if }\mbox{ else} | ||
| + | \end{cases}</math> | ||
Revision as of 21:43, 5 November 2009
TWO DIMENSIONAL SIGNALS
Some 2D signals are $ \ \delta\left (\mathit{x}, \mathit{y}\right ) $,Rect$ \left (\mathit{x}, \mathit{y}\right ) $,Sinc$ \left (\mathit{x}, \mathit{y}\right ) $.One important property of 2D functions is that they are separable,when they are a product of two 1D signals.They are of the form :
$ \ \mathbf{f}\left (\mathit{x}, \mathit{y}\right )=\mathbf{g}\left (\mathit{x}\right )\mathbf{h}\left (\mathit{y}\right) $
$ Rect<math>\left (\mathit{x}, \mathit{y}\right ) = <math> \begin{cases} 1, & \mbox{if }|x|&|y|\mbox{ is less than 1} \\ 0, & \mbox{if }\mbox{ else} \end{cases} $
