1. A dose rate measuring apparatus, comprising: a radiation detector that outputs an analog pulse for incident radiation; and a signal processing portion including (i) a wave height measuring function for converting the analog pulse inputted therein to a digital form and measuring a peak wave height of the analog pulse, and (ii) a wave height spectrum measuring function for measuring a wave height spectrum on a basis of measured wave height data, computing a dose rate and mean energy on a basis of measured wave height spectral data, and outputting computation results, wherein the signal processing portion is configured to compute the dose rate on the basis of the measured wave height spectral data in a wave height range and over a specified period of time, and to compute the mean energy on the basis of the measured wave height spectral data over the same wave height range and specified period of time.