Considering the problem of EBPSK signal demodulation, a new approach based on the wavelet scalogram using continuous wavelet transform is proposed. Our system is twofold: an adaptive wavelet construction method that replaces manual selection existing wavelets method and, on the other hand, a nonlinear demodulation system based on image processing and pattern classification is proposed. To evaluate the performance of the adaptive wavelet and compare the performance of the proposed system with the existing systems, a series of comprehensive simulation experiments is conducted under the environment of uniform white noise, colored noise, and additive white Gaussian noise channel, respectively. Simulation results of different wavelets show that the system using adaptive wavelet has lower bit error rate (BER). Moreover, simulation results of several systems show that the BER of the proposed system is the lowest among all systems, such as amplitude detection, integral detection, and some continuous wavelet transform systems (specific scales and times and maximum lines). In a word, the adaptive wavelet construction proposed in this paper yields superior performances compared with the manual selection, and the proposed system has better performances than the existing systems. Index terms are signal demodulation, adaptive wavelet, continuous wavelet transform, and BER.