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We propose and experimentally demonstrate a frequency down-converted and sensitivity enhanced fiber optic sensing technique based on a multi-passband microwave photonic filter (MPF) employing two cascaded fiber optic interferometers and dispersive medium. The frequency shift of the passband centered at high frequency where the sensing element is related can be down-converted to the frequency shift of low-frequency passband and enjoying narrower 3 dB bandwidth. And even greater frequency shift of passband located at low frequency have been achieved in our proposed fiber optic sensing system. Two interferometers, the Sagnac interferometer (SI), and the Mach–Zehnder interferometer (MZI) are used as a demonstration and the proof-of-concept experiments of temperature measurement are demonstrated, which show that our proposed fiber optic sensing system can down-converted the monitoring passband of SI based MPF from 687 MHz to 437 MHz, while enjoying narrower 3 dB bandwidth and maintaining the same sensitivity (0.81 MHz/°C) that of at 687 MHz, and thus bring convenience to detection. In addition, when taking the SI and MZI both as sensing elements, enhanced and adjustable sensitivity of sensing system can be achieved by adjusting the sensing fiber length of MZI. In our experiment, we have achieved enhanced and tailorable sensitivity from 0.81 MHz/°C to 8.44 MHz/°C, by monitoring the MPF's passband centered at low frequency of 437 MHz, which is about 1.59–16.55 times of the SI based single passband MPF centered at the similar frequency (446 MHz). Lower frequency and higher sensitivity can be obtained by designing the parameters of the fiber optic interferometers, which provides a powerful tool for high sensitivity, high-resolution, and low-cost fiber optic interferometer-based sensor systems.