盒式滤波器的失误之处

The gain that ripples

A wave the box cannot see

Boxes do not compose

Consequences for repeated blurs

For the three-tap box $[1,1,1]$ on a signal of length $N$, which statement about the gain $H[u] = \sin(3\pi u/N)/\sin(\pi u/N)$ is correct?

An image is blurred with the kernel $[1,1,1]$ and then blurred again with the same kernel, with no normalization in between. What is the combined kernel of the two passes?

The alternating wave $[1, -1, 1, -1]$ passes through the kernel $[1,1,1]$. Compute the output value at the position aligned with the third input sample, that is the sum $1 \times 1 + 1 \times (-1) + 1 \times 1$, and write the ratio of this output amplitude to the input amplitude $1$.