:<math> H(z) = \frac{1}{z^N} \sum_{m=0}^{M} b_m z^m = \sum_{m=0}^{M} b_m z^{-(N-m)} = \sum_{k=0}^{N} h[k] z^{-k} </math>
which implies that h[k] = b<sub>N-k</sub>. In other words, if you have the impulse response coefficients h[n] of a FIR filter, you enter them in the reverse order: h[0], h[1], ..., h[N-1], h[N], for the numerator array, and enter 1, 0, 0, ..., 0 for the denominator array. The figure below shows the reduced block diagram of the FIR digital filter.
<table>