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3.10 Frequency Response 77

Figure 3.14 Phase response for the third-order digital lowpass filter

3.10.4 Group Delay Function
An important issue in many applications is the delay associated with the process-
ing of a signal. A common measure of delay is the group delay, or envelop delay,
which is defined as

The group delay should be constant in applications where the waveform of the
signal is important—for example, in systems for obtaining an EGG (electrocardio-
gram). Images are particularly sensitive to variations in the group delay, but rela-
tively insensitive to variations in the magnitude function. Figure 3.15 shows the
group delay for the Cauer filter that was designed in Example 3.4.
The group delay can be expressed in terms of the transfer function which is
defined in section 3.11 (see Problem 3.15):