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A combined interrogation and signal processing technique which facilitates high-speed simultaneous static and dynamic strain demodulation of multiplexed fiber Bragg grating sensors is described. The scheme integrates passive, interferometric wavelength-demodulation and fast optical switching between wavelength division multiplexer channels with signal extraction via a software lock-in amplifier and fast Fourier transform. Static and dynamic strain measurements with noise floors of 1 nε and nε/√Hz, between 5 mHz and 2 kHz were obtained. An inverse analysis applied to a cantilever beam set up was used to characterize and verify strain measurements using finite element modeling. By providing distributed measurements of both ultra-high-resolution static and dynamic strain, the proposed scheme will facilitate advanced structural health monitoring.