An encoding apparatus for compressively encoding an original signal being a speech and audio signal by generating low-frequency-band encoding information from the original signal and high-frequency-band encoding information from the original signal and the generated low-frequency-band encoding information, wherein the encoding apparatus comprises the following sections for generating the high-frequency-band encoding information from the original signal: a first spectrum calculating section adapted to calculate a first spectrum of a signal obtained by decoding the generated low-frequency-band encoding information; a second spectrum calculating section adapted to calculate a second spectrum of the original signal; an amplitude adjusting section adapted to select an amplitude adjustment coefficient from a plurality of candidates prepared in advance and adjust the first spectrum using this amplitude adjustment coefficient as an exponent having a value, γ, where 0 ≤ γ ≤ 1, so that a ratio between a maximum amplitude spectrum and a minimum amplitude spectrum of an amplitude-adjusted first spectrum is closest to a dynamic range of a high frequency band of the second spectrum; the amplitude adjusting section being adapted to output an encoded code for the amplitude adjustment coefficient; a filter state setting section adapted to set the amplitude-adjusted first spectrum as an internal state of a pitch filter; a lag setting section adapted to sequentially output a lag T to a filtering section while changing the lag T within a search range set in advance in accordance with an instruction from a search section; the filtering section adapted to carry out filtering processing using the internal state of the pitch filter and the lag T, and calculate a first estimated original spectrum; a search section adapted to calculate a distortion E between the high frequency band of the second spectrum and the first estimated original spectrum, select a minimizing lag T which minimizes the distortion E by selecting the instruction, and output an encoded code for the minimizing lag T; an extension spectrum decoding section adapted to decode the encoded code for the amplitude adjustment coefficient and the encoded code for the minimizing lag T, and generate a second estimated original spectrum; a scale factor encoding section adapted to encode and output a scale factor of the second estimated original spectrum using the high frequency band of the second spectrum and the second estimated original spectrum. a first spectrum calculating section adapted to calculate a first spectrum of a signal obtained by decoding the generated low-frequency-band encoding information; a second spectrum calculating section adapted to calculate a second spectrum of the original signal; an amplitude adjusting section adapted to select an amplitude adjustment coefficient from a plurality of candidates prepared in advance and adjust the first spectrum using this amplitude adjustment coefficient as an exponent having a value, γ, where 0 ≤ γ ≤ 1, so that a ratio between a maximum amplitude spectrum and a minimum amplitude spectrum of an amplitude-adjusted first spectrum is closest to a dynamic range of a high frequency band of the second spectrum; the amplitude adjusting section being adapted to output an encoded code for the amplitude adjustment coefficient; a filter state setting section adapted to set the amplitude-adjusted first spectrum as an internal state of a pitch filter; a lag setting section adapted to sequentially output a lag T to a filtering section while changing the lag T within a search range set in advance in accordance with an instruction from a search section; the filtering section adapted to carry out filtering processing using the internal state of the pitch filter and the lag T, and calculate a first estimated original spectrum; a search section adapted to calculate a distortion E between the high frequency band of the second spectrum and the first estimated original spectrum, select a minimizing lag T which minimizes the distortion E by selecting the instruction, and output an encoded code for the minimizing lag T; an extension spectrum decoding section adapted to decode the encoded code for the amplitude adjustment coefficient and the encoded code for the minimizing lag T, and generate a second estimated original spectrum; a scale factor encoding section adapted to encode and output a scale factor of the second estimated original spectrum using the high frequency band of the second spectrum and the second estimated original spectrum.