The purpose of the present invention is to more efficiently extend, using a low bit rate, the bandwidth of input signals having a harmonics structure, in order to obtain better audio quality. The present invention is installed in a device that extends bandwidth for audio signal encoding and decoding. This novel bandwidth extension encoding identifies a low-frequency spectrum component having the highest correlation to a high-frequency bandwidth signal among input signals, duplicates a high-frequency spectrum by energy adjustment of said component, and maintains the harmonic relationship between the low-frequency spectrum and the duplicated high-frequency spectrum by adjusting the spectral peak position of the duplicated high-frequency spectrum, on the basis of a harmonic frequency estimated from a composite low-frequency spectrum.