This study aims to identify a method for classifying signals using their reduced sparse forms with a higher degree of accuracy. Many signals, such as sonar, radar, or seismic signals, are either sparse or can be made sparse in the sense that they have sparse or compressible representations when expressed in the appropriate basis. They have a convenient transform domain in which a small number of sparse coefficients express them as linear sums of sinusoidals, wavelets, or other bases. Although real-valued artificial neural networks (ANNs) have been frequently used in the classification of sonar signals for a long time, complex-valued wavelet neural network (CVWANN) is used for these complex reduced sparse forms of sonar signals in this study. Before the classification, the number of inputs was reduced to 1/3 dimension. Complex-valued sparse coefficients (CVSCs) obtained from the reduced form were classified by CVWANN. The performance of the proposed method is presented and compared to other classification methods. Our method, CVSCs + CVWANN, is very successful as 94.23% by tenfold cross-validation data selection and 95.19% by 50-50% training-testing data selection.