There is disclosed an encoding device capable of improving similarity between the high frequency band spectrum of the original signal and a new spectrum to be generated while realizing a low bit rate when encoding a wide-band signal spectrum. The encoding device has sub-band amplitude calculation units for calculating the amplitude of the respective sub-bands for the high frequency band spectrum obtained from the wide-band signal. A search unit and a gain codebook select some sub-bands from a plurality of sub-bands and only the gain of the selected sub-bands is subjected to encoding. An interpolation unit expresses the gain of the sub-band not selected, by mutually interpolating the selected gains.