The distinction between phase shift and time delay becomes very important when considering wideband signals. A single tone represented by a sinusoid having constant time delay and phase shift terms in the argument is shown in Figure 7.1. Phase shift and time delay are constants in the cosine argument. The phase shift is bound by
, while the time delay has no bounds. When dealing with only one frequency (narrow band), phase shift and time delay are identical. The phase shift associated with time delay (2πfTd) is a linear function of frequency and has a constant Fourier transform with respect to frequency as shown at the top of Figure 7.2. By contrast, the Fourier transform of a signal time delay is a linear function of frequency as shown at the bottom of Figure 7.2. As mentioned in Chapter 5, time delay is also known as group delay (envelope delay). Group delay is [1]
a measure of component phase distortion,
the signal transit time through a component as a function of frequency,
the negative of the rate of change of phase through a component.
FIGURE 7.1 Time delay and phase shift in the argument of a Fourier harmonic.
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, while the time delay has no bounds. When dealing with only one frequency (narrow band), phase shift and time delay are identical. The phase shift associated with time delay (2πfTd) is a linear function of frequency and has a constant Fourier transform with respect to frequency as shown at the top of Figure 7.2. By contrast, the Fourier transform of a signal time delay is a linear function of frequency as shown at the bottom of Figure 7.2. As mentioned in Chapter 5, time delay is also known as group delay (envelope delay). Group delay is [1]