This paper considers the use of online frequency response estimates for change detection, leading to fault detection and diagnosis. Spectral changes are detected as deviations in the frequency response, through the choice of a suitable observation variable. Taking into consideration the statistical nature of a finite-time estimator, a chi(2) fixed sample size detector is then designed. The detector is shown to be capable of detecting spectral changes for many classes of systems. The performance of the detector and some practical considerations involving robustness are discussed. Simulations and an implementation on a DC motor are used to illustrate the performance and properties of the detector.