 If the input is available column by column instead, we need to store formula_46 columns of the input.A zero phase filter with a real impulse response satisfies formula_68 = formula_69, which means that each sample can be paired with another of identical value.In this case we can use the arithmetic distributive law to interchange some of the multiplications and additions, to reduce the number of multiplications necessary to implement the filter, but the number of multiplications is still proportional to the filter order.