The phase response of a passband waveform at the receiver is given by $\phi(f) = -2\pi\alpha(f - f_c) - 2\pi\beta f_c$, where $f_c$ is the centre frequency, and $\alpha$ and $\beta$ are positive constants. The actual signal propagation delay from the transmitter to the receiver is

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β. A pure delay has phase response $\phi(f) = -2\pi f\tau$. Expanding the given expression shows the term proportional to $f$ has coefficient $-2\pi\alpha$, while the constant term shifts only the carrier phase. The actual propagation delay is therefore $\beta$ as indicated by the receiver phase form.

The phase response of a passband waveform at the receiver is given by \(\phi(f) = -2\pi\alpha(f - f_c) - 2\pi\beta f_c\), where \(f_c\) is the centre frequency, and \(\alpha\) and \(\beta\) are positive constants. The actual signal propagation delay from the transmitter to the receiver is

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