In this paper propose a multistage procedure to achieve good local resolution of significantly overlapping components in a transient signal. We assume the received transient signal to be a superposition of modulated and time-shifted versions of a single one-sided exponential function whose damping coefficient is known. At each stage of the proposed procedure we coarsely identify (as compared to the next stage) broad regions in the time-frequency (t-f) plane that have significant signal energy. These correspond to possible regions where signal components may be present. In each succeeding stage, they focus on these coarsely identified signal regions to further identify subregions in them that have significant energy. The detection of signal components in the sub-regions is done in the presence of possible interference from neighboring regions. Implementation of this method is based on the use of generalized eigenvectors of signal and interference correlation matrices. The detection statistics is a linear combination of the magnitude squared projections of the received data onto the individual generalized eigenvectors. © 1992 IEEE.