An encoding apparatus comprising: a down sampling section configured to performs down-sampling processing on an input speech/audio signal; a first encoding section (101, 102) configured to encode part of a low band that is a band lower than a predetermined frequency within the down-sampled input speech/audio signal to generate first encoded information; a first decoding section configured to decode the first encoded information to generate a first decoded signal; an up-sampling section configured to perform up-sampling processing on the first decoded signal; a delay section configured to store the input speech/audio signal in an internal buffer for a predetermined time and to output the delayed input speech/audio signal; and a filtering section configured to filter part of the low band of the first decoded signal or a calculated signal calculated using the first decoded signal, to obtain a band enhancement parameter as spectrum encoded information for obtaining part of a high band that is a band higher than the predetermined frequency of the input speech/audio signal, and to output said band enhancement parameter to a multiplexing section; a second encoding section configured to perform gain/shape quantization on a residual signal of the input speech/audio signal delayed by the delay section and the first decoded signal up-sampled by the up-sampling section, and to output obtained second encoded information to the multiplexing section; wherein the multiplexing section is configured to multiplex said first encoded information, second encoded information and band enhancement parameter and to obtain a bit data stream. a down sampling section configured to performs down-sampling processing on an input speech/audio signal; a first encoding section (101, 102) configured to encode part of a low band that is a band lower than a predetermined frequency within the down-sampled input speech/audio signal to generate first encoded information; a first decoding section configured to decode the first encoded information to generate a first decoded signal; an up-sampling section configured to perform up-sampling processing on the first decoded signal; a delay section configured to store the input speech/audio signal in an internal buffer for a predetermined time and to output the delayed input speech/audio signal; and a filtering section configured to filter part of the low band of the first decoded signal or a calculated signal calculated using the first decoded signal, to obtain a band enhancement parameter as spectrum encoded information for obtaining part of a high band that is a band higher than the predetermined frequency of the input speech/audio signal, and to output said band enhancement parameter to a multiplexing section; a second encoding section configured to perform gain/shape quantization on a residual signal of the input speech/audio signal delayed by the delay section and the first decoded signal up-sampled by the up-sampling section, and to output obtained second encoded information to the multiplexing section; wherein the multiplexing section is configured to multiplex said first encoded information, second encoded information and band enhancement parameter and to obtain a bit data stream.