There is disclosed an encoder apparatus whereby, when a band expanding technique for encoding, based on the spectral data of a lower frequency portion, the spectral data of a higher frequency portion is applied to a lower layer in a hierarchical encoding/decoding system, an efficient encoding can be performed in an upper layer as well, thereby improving the decoded-signal quality. In an encoder apparatus (101), a second layer decoder unit (207) calculates a spectrum (differential spectrum), which is to be encoded in a third layer encoder unit (210) that is an upper layer of the second layer decoder unit (207), by applying such an ideal gain (first gain parameter a1) that minimizes the energy of the differential spectrum.