Nuclear spectrum is one of the primary and most important information needed to obtain in the research work of high energy physics ,nuclear physics, heavy ion physics and nuclear technology application. The improvement and development of nuclear spectrum measurement method is a focus question for discussion all along in nuclear measure domain .The fast development of high speed ADC, various digital devices, real-time operate system (RTOS) and microprocessor laid the foundation for the appearance of new generation digital system and promoted the development and application of digital measurement system. Study on the new digital nuclear spectrum measurement system (DNSMS) have been the focus in the correlated field in the world.Based on the nuclear detector system output, a set of DNSMS includes waveform digital system (WDS) (include front-end conditioner (FEC), ADC device, data buffer and I/O interface), DSP system and result display and analysis (RDA) system. The research content of DNSMS include: study on the WDS, on the digital signals processing (DSP) system and on the implement principle and method of system. DSP is the core to develop the DNSMS, the author also concentrated on it.During the detector and preamplifier acquire nuclear information and WDS convert the analog signals to digit value, the nuclear signals will inevitable be distorted to make the final result worse. In the paper, the signal distorter was classified type A which was caused by the detector and preamplifier and type D caused by WDS, appropriate DSP algorithms were provided for diminishing or eliminating the influences of signal distortor upon spectrum resolution.In order to develop DNSMS easily and rapidly, a digital nuclear signal random generator (DNSRG) principle and algorithm was developed, and a corresponding windows application