In laser-driven inertial confinement fusion, hot electrons can preheat the fuel and prevent fusion-pellet compression to ignition conditions. Measuring the hot-electron population is key to designing an optimized ignition platform. The hot electrons in these high-intensity, laser-driven experiments, created via laser-plasma interactions, can be inferred from the bremsstrahlung generated by hot electrons interacting with the target. At the National Ignition Facility (NIF) [G. H. Miller, E. I. Moses, and C. R. Wuest, Opt. Eng. 43, 2841 (2004)], the filter-fluorescer x-ray (FFLEX) diagnostic-a multichannel, hard x-ray spectrometer operating in the 20-500 keV range-has been upgraded to provide fully time-resolved, absolute measurements of the bremsstrahlung spectrum with ∼300 ps resolution. Initial time-resolved data exhibited significant background and low signal-to-noise ratio, leading to a redesign of the FFLEX housing and enhanced shielding around the detector. The FFLEX x-ray sensitivity was characterized with an absolutely calibrated, energy-dispersive high-purity germanium detector using the high-energy x-ray source at NSTec Livermore Operations over a range of K-shell fluorescence energies up to 111 keV (U Kβ). The detectors impulse response function was measured in situ on NIF short-pulse (∼90 ps) experiments, and in off-line tests.