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| − | a) Since | + | a) Since |
<math>X(e^{j\mu},e^{j\nu}) = \sum_{m=-\infty}^{\infty} \sum_{n=-\infty}^{\infty} | <math>X(e^{j\mu},e^{j\nu}) = \sum_{m=-\infty}^{\infty} \sum_{n=-\infty}^{\infty} | ||
| − | x(m,n)e^{-j(m\mu+n\nu)}</math> | + | x(m,n)e^{-j(m\mu+n\nu)}</math><br> |
| − | and | + | and |
<span class="texhtml"><math>p_0(e^{jw}) = \sum_{m=-\infty}^{\infty} \sum_{n=-\infty}^{\infty} | <span class="texhtml"><math>p_0(e^{jw}) = \sum_{m=-\infty}^{\infty} \sum_{n=-\infty}^{\infty} | ||
| − | x(m,n)e^{-jnw}</math>， </span> | + | x(m,n)e^{-jnw}</math>， </span> |
| − | we have: | + | we have: |
| − | < | + | <span class="texhtml">''P''<sub>0</sub>(''e''<sup>''j''''w'''</sup>''') = ''X''(''e''<sup>''j''μ</sup>,''e''<sup>''j'''</sup>'''''w'') | <sub>μ</sub> = 0</span> |
Revision as of 21:25, 10 November 2014
a) Since
$ X(e^{j\mu},e^{j\nu}) = \sum_{m=-\infty}^{\infty} \sum_{n=-\infty}^{\infty} x(m,n)e^{-j(m\mu+n\nu)} $
and
$ p_0(e^{jw}) = \sum_{m=-\infty}^{\infty} \sum_{n=-\infty}^{\infty} x(m,n)e^{-jnw} $，
we have:
P0(ej'w) = X(ejμ,ejw) | μ = 0
