Consider the roof edge pattern: Consider the roof edge pattern: what happen to the edge if it filtered with a low-pass filter \begin{tabular}{|l|l|l|} \hline \( 1 / 9 \) & \( 1 / 9 \) & \( 1 / 9 \) \\ \hline \( 1 / 9 \) & \( 1 / 9 \) & \( 1 / 9 \) \\ \hline \( 1 / 9 \) & \( 1 / 9 \) & \( 1 / 9 \) \\ \hline \end{tabular} \begin{tabular}{|l|l|l|l|l|l|l|l|l|l|} \hline 30 & 30 & 30 & 120 & 120 & 120 & 120 & 60 & 60 & 60 \\ \hline 30 & 30 & 30 & 120 & 120 & 120 & 120 & 60 & 60 & 60 \\ \hline 30 & 30 & 30 & 120 & 120 & 120 & 120 & 60 & 60 & 60 \\ \hline 30 & 30 & 30 & 120 & 120 & 120 & 120 & 60 & 60 & 60 \\ \hline 30 & 30 & 30 & 120 & 120 & 120 & 120 & 60 & 60 & 60 \\ \hline \end{tabular} \begin{tabular}{|l|l|l|l|l|l|l|l|l|l|} \hline 30 & 30 & 60 & 90 & 120 & 120 & 100 & 80 & 60 & 60 \\ \hline 30 & 30 & 60 & 90 & 120 & 120 & 100 & 80 & 60 & 60 \\ \hline 30 & 30 & 60 & 90 & 120 & 120 & 100 & 80 & 60 & 60 \\ \hline 30 & 30 & 60 & 90 & 120 & 120 & 100 & 80 & 60 & 60 \\ \hline 30 & 30 & 60 & 90 & 120 & 120 & 100 & 80 & 60 & 60 \\ \hline \end{tabular}
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The filter is a 3x3 matrix where each element is \( \frac{1}{9} \). This is an averaging filter that will smooth the image by averaging the values of each 3x3 neighborhood. Show more…
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Returning to Fig. 13.37 , what kind of spatial filter would produce each of the patterns shown in Fig. P.13.43?
y(t) = x(t) - x(t-1). The frequency response of the filter with the input-output relationship amplitude spectrum, |H(jw)|, needs to be found and roughly drawn. What kind of filter is this (Lowpass, Band-pass, High-pass)? Why is that?
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