The main aspect of the paper is to give an answer to the question of what specific kind of defect has actually occurred in a structure and how to distinguish between different kinds of discontinuities. For this purpose composite rods and beams with fatigue cracks, step changes in cross-sectional area and small changes in material properties have been investigated. The objective of the work has been to propose a signal processing methodology based on wavelet transformation for identification of specific discontinuity. The identification of a fatigue crack from other discontinuities has been demonstrated. It has been also found that the proposed methodology might be useful for precise indication of the size of the identified fatigue damage.