$ \pi $-Phase Filters

Under our definition, a zero-phase filter always has a real, even impulse response [ $ h(n) = h(-n)$], but not every real, even, impulse response is a zero-phase filter. For example, if $ h(n)$ is zero phase, then $ -h(n)$ is not; however, we could call $ -h(n)$ a ``$ \pi $-phase filter'' if we like (a zero-phase filter in series with a sign inversion).

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Implementation of Repeated Poles