Consider a 3x3 spatial mask that averages the four closet neighbours of a point

(x, y), but excludes the point itself from the average.

i) Find the equivalent filter, H (u, v), in the frequency domain.

ii) Show that your result is a lowpass filter.

i) The spatial mask described averages the four closest neighbors of a point (x, y), excluding the point itself. To express this in mathematical terms, the mask M(x,y)M(x, y) can be represented as:

M(x,y)=[0140140140140]M(x, y) = \begin{bmatrix} 0 & \frac{1}{4} & 0 \\ \frac{1}{4} & 0 & \frac{1}{4} \\ 0 & \frac{1}{4} & 0 _________ ___ ________ ___ __________ ______ ________ ____ ________ ________.
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