This is a well known trick. See “Filter Realization” section here: https://en.m.wikipedia.org/wiki/Digital_filter https://en.m.wikipedia.org/wiki/Digital_filter

This is a well known trick. See “Filter Realization” section here: https://en.m.wikipedia.org/wiki/Digital_filter https://en.m.wikipedia.org/wiki/Digital_filter High-order polynomials are very sensitive to small deltas in the coefficients of their high-order terms. Representing the same function as the product of low-order factors is much more stable numerically.