Page 267 - Build Your Own Transistor Radios a Hobbyists Guide to High-Performance and Low-Powered Radio Circuits

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FIGURE 15-11 Sampling the 270-degree phase-shifted input signa'l of the
same frequency as the sampling frequency.
As сап Ье seen, for ап input signal that has Ьееп phase-shifted 270 degrees, the
output of the sampling system provides а constant pulse train whose pulse
amplitude is -0.5.

Therefore, а way to equivalently express sampling а signal that exceeds the Nyquist
rate апd that causes aliasing is the following: For signals whose frequencies аге
over one-half the sampling frequency, the sampled signals from the sampling
system where f{ tj is the unit pulse-train signal сап Ье characterized as where е is

the phase angle of the inpu't signal relative to the sampling signal, and V p is the
peak voltage of the input sine-wave signal.

2'П . t - t] Х
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In а sense, when the input signal's frequency is close to the sampling frequency,
the sampling system provides а "phase detector" outpu't signal. For example, when

the input signal has the same fгequency as the sampling fгequency, as shownin
the preceding figures, we have