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$ \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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``Introduction to Digital Filters with Audio Applications'', by Julius O. Smith III, (September 2007 Edition).
Copyright © 2014-03-23 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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