A decoding apparatus comprising: a gain readout unit configured to read out encoded gain values at at least two gain sample positions (G31, G32) of a time series signal, representing an audio signal, and gain inclination values (D31, D32) indicating inclination of the gain values at the gain sample positions (G31, G32); an interpolation information readout unit configured to read out interpolation information indicating whether the gain value at each sample position (G31, G32) of the time series signal is obtained through linear interpolation or obtained through non-linear interpolation; an operation unit configured to obtain, at the two gain sample positions (G31, G32), straight lines (L51, L52) having the gain values at the gain sample positions (G31, G32) and having inclination indicated by the gain inclination values (D31, D32) at the gain sample positions (G31, G32), to obtain a position of an intersection of the straight lines (L51, L52) between the two gain sample positions (G31, G32) and to obtain differences between a gain value at the intersection obtained for the two gain sample positions (G32, G32) and the gain values at the two gain sample positions (G31, G32); and an interpolation processing unit configured to obtain a gain value at each sample position located between the two gain sample positions (G31, G32), through linear interpolation when the interpolation information is information indicating that the gain value is obtained through linear interpolation; and, based on the gain values at the gain sample positions (G31, G32) including the position of the intersection through linear interpolation or based on the gain values at the gain sample positions (G31, G32) through non-linear interpolation according to the differences when the interpolation information is information indicating that the gain value is obtained through non-linear interpolation, wherein the linear interpolation based on the gain values at the gain sample positions (G31, G32) including the position of the intersection comprises obtaining a waveform constituted with the straight lines (L51, 52) respectively connecting the intersection and the gain sample positions (G31, G32). a gain readout unit configured to read out encoded gain values at at least two gain sample positions (G31, G32) of a time series signal, representing an audio signal, and gain inclination values (D31, D32) indicating inclination of the gain values at the gain sample positions (G31, G32); an interpolation information readout unit configured to read out interpolation information indicating whether the gain value at each sample position (G31, G32) of the time series signal is obtained through linear interpolation or obtained through non-linear interpolation; an operation unit configured to obtain, at the two gain sample positions (G31, G32), straight lines (L51, L52) having the gain values at the gain sample positions (G31, G32) and having inclination indicated by the gain inclination values (D31, D32) at the gain sample positions (G31, G32), to obtain a position of an intersection of the straight lines (L51, L52) between the two gain sample positions (G31, G32) and to obtain differences between a gain value at the intersection obtained for the two gain sample positions (G32, G32) and the gain values at the two gain sample positions (G31, G32); and an interpolation processing unit configured to obtain a gain value at each sample position located between the two gain sample positions (G31, G32), through linear interpolation when the interpolation information is information indicating that the gain value is obtained through linear interpolation; and, based on the gain values at the gain sample positions (G31, G32) including the position of the intersection through linear interpolation or based on the gain values at the gain sample positions (G31, G32) through non-linear interpolation according to the differences when the interpolation information is information indicating that the gain value is obtained through non-linear interpolation, wherein the linear interpolation based on the gain values at the gain sample positions (G31, G32) including the position of the intersection comprises obtaining a waveform constituted with the straight lines (L51, 52) respectively connecting the intersection and the gain sample positions (G31, G32).