Methods and systems for x-ray inspection of an object using pulses whose spectral composition varies during the course of each pulse. A temporal sequence of pulses of penetrating radiation is generated such that the spectral content of each pulse evolves with time. The pulses are formed into a beam that is scanned across the object and detected after traversing the object. The detector signal is processed to derive at least one material characteristic of the object, such as effective atomic number, on the basis of temporal evolution of the detector signal during the course each pulse of the sequence of pulses. The time intervals may be predetermined, or else adapted based on features of the detected signal.