A decoding apparatus comprising: a demultiplexing device configured to demultiplex input encoded data into low-frequency encoded data and high-frequency encoded data; a low-frequency signal generating device configured to decode the low-frequency encoded data to generate a low-frequency signal; a sub-band dividing device configured to divide the low-frequency signal into a plurality of low-frequency sub-bands each corresponding to one of a plurality of sub-band indices to generate a low-frequency sub-band signal for each of the low-frequency sub-bands; a feature amount calculating device configured to calculate a low-frequency sub-band power for each of the low-frequency sub-bands using the low-frequency sub-band signal; a high-frequency decoding device configured to decode the high-frequency encoded data to obtain a coefficient index and output, based on the obtained coefficient index, one of a plurality of estimating coefficients prepared beforehand regarding each of a plurality of high-frequency sub-bands making up a band of the high-frequency signal; a high-frequency sub-band power calculating device configured to calculate a high-frequency sub-band power of a high-frequency sub-band signal of a high-frequency signal by multiplying the low-frequency sub-band powers by the outputted estimating coefficient, and obtaining the sum of the low-frequency sub-band powers by which the outputted estimated coefficient has been multiplied; a high-frequency signal generating device configured to generate the high-frequency signal using the high-frequency sub-band power and the low-frequency sub-band signal; and a synthesizing device configured to synthesize the low-frequency signal generated by the low-frequency signal generating device and the high-frequency signal generated by the high-frequency signal generating device and to output a synthesized signal. a demultiplexing device configured to demultiplex input encoded data into low-frequency encoded data and high-frequency encoded data; a low-frequency signal generating device configured to decode the low-frequency encoded data to generate a low-frequency signal; a sub-band dividing device configured to divide the low-frequency signal into a plurality of low-frequency sub-bands each corresponding to one of a plurality of sub-band indices to generate a low-frequency sub-band signal for each of the low-frequency sub-bands; a feature amount calculating device configured to calculate a low-frequency sub-band power for each of the low-frequency sub-bands using the low-frequency sub-band signal; a high-frequency decoding device configured to decode the high-frequency encoded data to obtain a coefficient index and output, based on the obtained coefficient index, one of a plurality of estimating coefficients prepared beforehand regarding each of a plurality of high-frequency sub-bands making up a band of the high-frequency signal; a high-frequency sub-band power calculating device configured to calculate a high-frequency sub-band power of a high-frequency sub-band signal of a high-frequency signal by multiplying the low-frequency sub-band powers by the outputted estimating coefficient, and obtaining the sum of the low-frequency sub-band powers by which the outputted estimated coefficient has been multiplied; a high-frequency signal generating device configured to generate the high-frequency signal using the high-frequency sub-band power and the low-frequency sub-band signal; and a synthesizing device configured to synthesize the low-frequency signal generated by the low-frequency signal generating device and the high-frequency signal generated by the high-frequency signal generating device and to output a synthesized signal.