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In this study, automatic recognition of digitally modulated signals is investigated using the Continuous Wavelet Transform (CWT) in conjunction with techniques typically used in pattern recognition. In particular, the method of template matching is used. The templates used for the Automatic Modulation Recognition (AMR) process are determined based on the features, i.e., fractal patterns in the scalograms, of specific modulation schemes as they appear in the Wavelet Domain (WD). The digital modulation schemes considered include both binary and quaternary Amplitude (ASK) and Frequency Shift Keying (FSK), as well as M-ary Phase Shift Keying (MPSK) signals, where M=2, 4, and 8. The modulated signals used in this study have been corrupted by Additive White Gaussian Noise (AWGN) resulting in Signal-to-Noise Ratios (SNRs) in the range of -5 dB to 10 dB. Through the use of Monte Carlo computer simulations, it has been determined that the average overall correct classification rate for M-ary PSK signals was 99.1%; 98.9% for BASK and 4-ASK signals; and 90.4% for BFSK and 4-FSK signals over the range of SNR values.