This Small Business Innovation Research (SBIR) Phase I project aims to develop a novel broadband digital spectrometer for radio-frequency receivers, with particular application to an imaging spectrometer for sub-millimeter-wave astronomy. For optimum performance, such a receiver will make use of a cryogenic mixer to generate an intermediate-frequency output ~1 GHz. A spectrometer that can accept this type of mixer output and then generate the signal power spectrum with frequency resolution ~1 MHz is proposed. The core of this spectrometer will be a fast, sensitive analog-to-digital converter and a digital auto-correlator based on rapid-single-flux-quantum (RSFQ) digital logic, designed to operate with a commercial cryo-cooler at a temperature of 4 K. Other components of this receiver, such as multiplexers to combine pixel outputs, have already been developed. These components will be integrated monolithically on the same niobium integrated circuit<br/><br/>The auto-correlator has extensive applications in RF communications and image-processing systems currently limited by the speed of digital processing. Some of these applications include Code Division Multiple Access (CDMA) communications, advanced instrumentation for ground-based and space-based spectroscopy and signal analysis are further enabled by the combination of the proposed auto-correlator with recent advances in the manufacturing of affordable cryo-coolers. The digital-RF base station target, where the auto-correlator would be used for load management, and its close relative, the cross-correlator could be used for reducing multi-path distortion. The digital-RF base station with software radio architecture represents a multi-billion dollar market, from which even a small market share will be worthwhile pursuing.