To provide a band-division type encoding/decoding method with which compressibility can be increased without deteriorating auditory sound quality so much or the auditory sound quality can be improved while nearly the same compressibility is maintained, and a decoding device used for the method.

An encoder-1 side performs down-sampling before band division to decrease the amount of data and a decoder-2 side performs up-sampling after band integration to restore a signal by a digital filter 24 designed under sample value H∞ control. In a method for designing the filter, a conditional expression is so set that the error signal ec of the continuous time between a signal obtained by adding time delay to a signal generated by limiting the band of an input analog signal we and the restored signal zc passed through an over-sampling D/A conversion part becomes small, and the conditional expression is converted into a finite-dimensional discrete time system to obtain an approximate calculation expression. After conditions of the filter etc., are determined, the calculation expression is solved as the problem of H∞ control being one method of sample value designing. Consequently, a frequency component lost in the down-sampling can be restored to an extent where there is no auditory problem.