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Phase-encoded optical sampling allows radio-frequency and microwave signals to be directly down-converted and digitized with high linearity and greater than 60-dB (10-effective-bit) signal-to-noise ratio. Wide-band electrical signals can be processed using relatively low optical sampling rates provided that the instantaneous signal bandwidth is less than the Nyquist sampling bandwidth. We demonstrate the capabilities of this technique by using a 60-MS/s system to down-sample two different FM chirp signals: 1) a baseband (0-250 MHz) linear-chirp waveform and 2) a nonlinear-chirp waveform having a 10-GHz center frequency and a frequency excursion of 1 GHz. We characterize the frequency response of the technique and quantify the analog bandwidth limitation due to the optical pulse width. The 3-dB bandwidth imposed by a 30-ps sampling pulse is shown to be 10.4 GHz. We also investigate the impact of the pulse width on the linearity of the phase-encoded optical sampling technique when it is used to sample high-frequency signals.