The purpose of this work is to begin the development of a comprehensive time/frequency spectral analysis approach that can be applied to complex signals associated with real world systems, such as rotating machinery. Rotating machinery operating at nominally constant speed comprise a large class of important real world systems that have received relatively little attention in terms of stochastic characterizations of any greater sophistication than those associated with wide sense stationary processes. In this work, a periodic-time/frequency characterization procedure is introduced in the context of vibration analysis associated with a diesel engine operating at nominally constant speed. This application highlights a number of difficulties, such as the need for accurate period estimation, accommodation of noninteger periods in relation to digital processing, and identification and separation of tonal components from the signature in order to arrive at a more parsimonious characterization. A theorem relating to the limiting influence of these difficulties is presented. These difficulties are addressed using advanced signal processing tools, such as a recently developed tone identification procedure and extended Kalman filtering, which to the authors' knowledge have not been considered to date in such a setting. Results include a simple correction algorithm for noninteger periods, excellent separation of tonal components whose frequencies are slowly varying, and subsequently a modest improvement in the spectral characterization of the remainder of the process. These results have some significance in relation to diesel engine vibration, since they unambiguously identify tonal vibration components, in addition to a random structure which appears to include random excitation of resonances.