Example

It is easy to classify completely all first-order FIR filters:

$$H(z) = 1 + h_1 z^{-1}$$

where we have normalized $h_0$ to 1 for simplicity. We have a single zero at $z=-h_1$ . If $\left\vert h_1\right\vert< 1$ , the filter is minimum phase. If $\left\vert h_1\right\vert>1$ , it is maximum phase. Note that the minimum-phase case is the one in which the impulse response $[1,h_1,0,\ldots]$ decays instead of grows. It can be shown that this is a general property of minimum-phase sequences, as elaborated in the next section.