Filters Preserving Phase

In this chapter, *linear phase* and *zero phase* filters are
defined and discussed.

When one wishes to modify only a signal's magnitude-spectrum and not
its spectral phase, then a *linear-phase filter* is
desirable. (The name *linear-phase-response filter* would be more
precise.) Linear-phase filters have a *symmetric impulse
response*, *i.e.*,

We will show that every symmetric impulse response corresponds to a
*real* frequency response times a
*linear phase term*
, where
is the *slope* of the linear phase. Linear phase is
often ideal because a filter phase of the form
corresponds to phase delay

- Zero-Phase Filters
- Example Zero-Phase Filters
- Odd Impulse Reponses
- Symmetric Linear-Phase Filters
- Example Linear-Phase Filters
- Antisymmetric Linear-Phase Filters
- Forward-Backwards Filtering
- Phase Distortion at Passband Edges

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Center for Computer Research in Music and Acoustics (CCRMA), Stanford University

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