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A novel photonic approach to simultaneously implement frequency measurement and signal separation is proposed and experimentally demonstrated for pulsed and continuous-wave (CW) microwave signals. In this approach, a light wave is externally modulated with carrier suppressed by a pulsed or CW microwave signal to be measured, and then sent to two optical complementary filters to perform frequency-to-amplitude mapping. The outputs of the two filters are detected by low-speed photodetectors, low-frequency alternating currency (AC) electronic component and direct current (DC) one being generated. The carrier frequency of the pulsed microwave signal can be estimated by monitoring the power of the AC component, while the frequency of the CW microwave signal is discriminated from the power of the DC component, with the frequency measurement and the signal separation simultaneously realized. In proof-of-concept experiments, within the frequency range from 5 to 20 GHz, measurement errors less than ±0.1, ±0.11 , or ±0.13 GHz are achieved for a pulsed signal with pulse repetition frequency of 0.25, 0.5, or 1 MHz, whereas the errors less than ±0.08 GHz are derived for a CW signal.