Boundaries and Padding

The border asks for missing samples

Zero, circular and mirror

Mirror wins against ground truth

You must blur a large natural photograph near its edges with a wide box kernel. Which padding choice best matches what the blur would look like if you had photographed a wider view?

In circular convolution the kernel index is read modulo N, as in $h[(n-k)_N]$. With $N = 6$, $n = 1$ and $k = 4$, which kernel index is used?

A signal begins with the values $[5, 7, 9]$. With mirror padding, the phantom sample immediately to the left of the array reflects the first real sample's neighbor. Write the value of the first phantom sample to the left of the array.