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The instantaneous frequency of a rapidly tuned continuous-wave (CW) laser is measured through linear optical sampling against dual-frequency combs. This dual-comb interferometer determines the instantaneous frequency of the CW laser during a quasi-sinewave frequency sweep of 3 THz amplitude with a 10 ms period. More complicated waveforms are also measured with instantaneous chirps exceeding 1500 THz/s (12 000 nm/s). The uncertainty is 1.5 MHz at 20 ns time resolution, averaging down to 5 kHz at 5 μs time resolution. The absolute frequency accuracy can be calibrated to within 2.5 kHz provided there is a brief period (<;1 ms) of low laser chirp (<;160 GHz/s) during the waveform measurement to allow for a dual-comb Vernier measurement of the absolute frequency, modulo 3 THz. This approach allows for the characterization of arbitrary CW waveforms with instantaneous frequencies that change rapidly and over wide optical bandwidth.