Phase and Group Delay

In the previous sections we looked at the two most important frequency-domain representations for LTI digital filters, the transfer function and the frequency response:

We looked further at the polar form of the frequency response , thereby breaking it down into the amplitude response times the phase-response term .

In the next two sections we look at two alternative forms of the phase response: phase delay and group delay. After considering some examples and special cases, poles and zeros of the transfer function are discussed in the next chapter.

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Subsections

• Phase Delay
• Phase Unwrapping
• Group Delay
  • Derivation of Group Delay as Modulation Delay
  
  
• Group Delay Examples in Matlab
• Vocoder Analysis
• Numerical Computation of Group Delay

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written by 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.