Methods and apparatuses for encoding a signal and decoding a signal and a system for encoding and decoding are provided. The method for encoding a signal includes performing a classification decision process on high frequency signals of input signals, adaptively encoding the high frequency signals according to the result of the classification decision process, and outputting a bitstream including codes of low frequency signals of the input signals, adaptive codes of the high frequency signals, and the result of the classification decision process. The classification decision process is performed on the high frequency signals, and adaptive encoding or adaptive decoding is performed according to the result of the classification decision process, so the quality of voice and audio output signals is improved.