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Embedded SystemsFPGAElectronics

Mathematics of the DFT
    Fourier Theorems for the DFT
       Fourier Theorems
          Shift Theorem
             Zero Phase Signals

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Zero Phase Signals

A zero-phase signal is thus a linear-phase signal for which the phase-slope $ \Delta$ is zero. As mentioned above (in §7.4.3), it would be more precise to say ``0-or-$ \pi $-phase signal'' instead of ``zero-phase signal''. Another better term is ``zero-centered signal'', since every real (even) spectrum corresponds to an even (real) signal. Of course, a zero-centered symmetric signal is simply an even signal, by definition. Thus, a ``zero-phase signal'' is more precisely termed an ``even signal''.


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Next: Application of the Shift Theorem to FFT Windows

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About the Author: Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.


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