Pulsed ionizing radiation fields are widely used in medical sector but can also be found in many other workplaces such as nondestructive testing. They are predominantly produced by pulsed X-ray generators and particle accelerators. In a recent literature, dealing with performance investigation of the commercial area dosimeters, it has been reported that none of the tested dosimeters yielded with satisfactory results for the dose rate measurements in pulsed fields. Such poor performance of commercial meters motivated us to develop a novel silicone photomultiplier (SiPM) based thallium doped sodium iodine photon detector system specifically designed to use a short time constant, and thus, enable dose rate measurements in pulsed photon radiation fields. The time constant plays a very important role in measurements of pulsed radiation fields. Decreasing the time constant increases the coefficient of variation of the measurement, while increasing the time constant will cause an error in case of short radiation pulse width. In scope of this work, we have developed the ambient dose equivalent rate calculation algorithm (for the scintillation detectors) with adaptive time constant to minimize total measurement error. The algorithm measures the X-ray pulse width employing the time-over-threshold measurement of the Hilbert transform of the detector signal. This measurement is then used for determining a time constant that defines a time window over which collected charge is derived. Calibration is applied to the derived signal and the dose rate is obtained. In case that statistically significant measurement could not be achieved due to too small value of the product of the time constant and the dose rate, algorithm will issue a warning. To obtain the evaluation signals, our SiPM detector was used. Signals from the detector were digitized with Rigol DS1104Z oscilloscope using 10 MHz sample rate, 24 Mpts of memory and stored for offline analysis. Algorithm was successfully evaluated trough different exposure scenarios to the pulsed X-ray generator.