When encoding an audio signal, it is possible to efficiently encode the audio signal while maintaining high register signal components, and prevent deterioration of sound quality of decoded signal. A digital audio signal is divided into a plurality of frequency bands. The digital audio signal having been divided into each band is function-approximated for each divided band. Further, parameters of function having been function-approximated are encoded. When performing decoding process, parameters of the function of each band are used to perform function interpolation, synthesize the function-interpolated signal of each band interpolated, and decode the signal. Thus, when function-approximating each band, by suitably setting the function equation, it is possible to perform an encoding process while maintaining the high register components and perform a compression-coding process which enables reproduction with very good sound quality.