Linear Phase Terms Next  |  Prev  |  Up  |  Top  |  Index  |  JOS Index  |  JOS Pubs  |  JOS Home  |  Search

#### Linear Phase Terms

The reason is called a linear phase term is that its phase is a linear function of frequency: Thus, the slope of the phase, viewed as a linear function of radian-frequency , is . In general, the time delay in samples equals minus the slope of the linear phase term. If we express the original spectrum in polar form as where and are the magnitude and phase of , respectively (both real), we can see that a linear phase term only modifies the spectral phase : where . A positive time delay (waveform shift to the right) adds a negatively sloped linear phase to the original spectral phase. A negative time delay (waveform shift to the left) adds a positively sloped linear phase to the original spectral phase. If we seem to be belaboring this relationship, it is because it is one of the most useful in practice.

Definition: A signal is said to be a linear phase signal if its phase is of the form where is any real constant, and is an indicator function which takes on the values 0 or over the points , .

A zero-phase signal is thus a linear phase signal for which the phase-slope is zero.

As mentioned above (in §7.4.3), it would be more precise to say piecewise constant phase'' instead of zero phase''. Similarly, linear phase'' is better described as linear phase interrupt by discontinuities.''

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