Given a 4 ×4 image, find the 4 ×4 lowpass filtered output using the 3 ×3 averaging filter with t

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Step 1: Extend the borders periodically
We need to extend the borders of the image to apply the

Given a $4 \times 4$ image, find the $4 \times 4$ lowpass filtered output using the $3 \times 3$ averaging filter with the borders periodically extended. $$ x(m, n)=\left[\begin{array}{llll} 45 & 78 & 87 & 51 \\ 59 & 56 & 62 & 49 \\ 59 & 39 & 44 & 57 \\ 56 & 36 & 35 & 51 \end{array}\right] $$