二项式滤波器

Pascal's triangle is a convolution engine

Closure, this time exact

The checkerboard wave dies exactly

The two-dimensional default

The binomial kernels come from repeated convolution of one-one. Why does $b_2 \circ b_3 = b_5$ hold exactly while the same statement fails for sampled Gaussians?

Why is the exact zero of $[1,2,1]$ at the alternating wave more valuable than the sampled Gaussian's strong but incomplete attenuation there?

The binomial kernel $b_2$ is convolved with the binomial kernel $b_3$. Write the index of the resulting binomial row $b_n$ as a number.