FIR difference equation vs convolution summation
I should have read further before asking this question! Anyway, I've found out that there are different ways to implement the FIR system as mathematically described in Equation 7.2.1 in the post above. Among these realizations/structures is the direct-form, which is the simplest to begin with. Equation 7.2.4 shows the transformation of the general equation in 7.2.1 in accordance with the direct-form.