Recognition of CW Morse signals can be divided into several phases such as detection of tones and spaces, signal processing for removing noise from detected signals, decision of tones/spaces, mapping a sequence of tones and spaces into characters, error correction of a character message with textual repetition. In this paper, in order to cope with signal fading effectively we propose a signal detection method of identifying peaks in the frequency domain and present techniques for combining multiple frequency peaks and for removing residual signal components and noise. LMS adaptive method is applied for decision of tones/spaces, and initial value setting and malfunctioning conditions are analyzed. In recognition experiments, we used CW Morse signals collected by radio receivers and found that the proposed method achieves good recognition performance even in severe fading conditions.