The paper indicates, for the benefit of system designers, how and to what extent independently available information — or generic characteristics derived from the signal itself — can be used to enhance the extraction of wanted signals in the presence of noise or interference. To bring out the commonalities in apparently different problems or methods, it uses the ‘state-space’ concept, common to the dimensions of time, frequency, antenna aperture and image space, and it treats signal processing as a sequence of transformations subject to a set of limiting constraints.