Morlet wavelets do not satisfy the permissibility condition of wavelet analysis, and there are therefore no inverse transformations for Morlet wavelet transforms. In this paper, we put forward the Yang and Pan transform (YPT), which is an adaptive discrete analysis method for shock signals. First, we improved the Morlet wavelet so that the centre and radius of the frequency window can be easily adjusted in the frequency domain. Second, we proposed the extremum frequency concept and analysed the extremum situation of the improved Morlet wavelet. Third, combining the improved Morlet wavelet and extremum frequency, we advanced the theory of the YPT, which does not need to satisfy the permissibility condition. We then continued by using a smoothing operator that can smooth the potentially distorted signal reconstructed after being analysed by the YPT and filtered by using the threshold filtering theory. This operator proved to be simple and efficient. Finally, a noisy signal was reconstructed after being analysed and filtered using the YPT and threshold filtering, respectively, to verify the validity of the theory, and the YPT was compared with the discrete wavelet transform (DWT). As a supplement to the theory in engineering, the shock signals about a gun automatic mechanism were also analysed using the theory in this paper. Good results were obtained, thereby demonstrating that the YPT can be helpful to further extract the features of shock signals in pattern recognition and fault diagnosis.

Shock signal features must be extracted for use in pattern recognition or fault diagnosis. In this work, we proposed a method for the feature extraction of shock signals, which are vibration signals that change faster and have larger amplitude ranges than general signals. First, we proposed the concepts of amplitude density for monotonic functions and piecewise monotonic functions. On the basis of these concepts, we then proposed the concept of the upper limit of density integral (ULDI), which was adopted to obtain signal features. Then, we introduced two types of serious fault cracks to the latch sheet of an automatic gun mechanism that is used on warships. Next, we applied the proposed method to extract the features of shock signals from data acquired when the automatic gun mechanism fired with normal and two fault patterns. Finally, we verified the effectiveness of our proposed method by applying the features that it extracted to a support vector machine (SVM). Our proposed method provided good results and was superior to the traditional statistics-based feature extraction method when applied to a SVM for classification. In addition, the former method demonstrated better generalisation than the latter. Thus, our method is an efficient approach for extracting shock signal features in pattern recognition and fault diagnosis.