A signal processing apparatus comprising: a demultiplexing unit that demultiplexes input encoded data into data including information on a segment including frames in which the same coefficient as a coefficient used in producing a high band signal is selected in a section to be processed including a plurality of frames, and coefficient information for obtaining the coefficient selected in the frames of the segment, and low band encoded data; a low band decoding unit that decodes the low band encoded data to produce a low band signal; a selection unit that selects a coefficient of a frame to be processed based on the coefficient information; a high band sub-band power calculation unit that calculates a high band sub-band power of a high band sub-band signal of each sub-band constituting the high band signal of the frame to be processed based on a low band sub-band power of a low band sub-band signal of a plurality of sub-bands constituting the low band signal of the frame to be processed and the selected coefficient; and a high band signal production unit that produces the high band signal of the frame to be processed based on the high band sub-band power and the low band sub-band signal; wherein: the data further includes reuse information indicating whether the coefficient of an initial frame in the section to be processed is the same as the coefficient of a frame just before the initial frame, and when the data includes the reuse information indicating that the coefficients are the same, the data does not include coefficient information of the initial segment of the section to be processed. a demultiplexing unit that demultiplexes input encoded data into data including information on a segment including frames in which the same coefficient as a coefficient used in producing a high band signal is selected in a section to be processed including a plurality of frames, and coefficient information for obtaining the coefficient selected in the frames of the segment, and low band encoded data; a low band decoding unit that decodes the low band encoded data to produce a low band signal; a selection unit that selects a coefficient of a frame to be processed based on the coefficient information; a high band sub-band power calculation unit that calculates a high band sub-band power of a high band sub-band signal of each sub-band constituting the high band signal of the frame to be processed based on a low band sub-band power of a low band sub-band signal of a plurality of sub-bands constituting the low band signal of the frame to be processed and the selected coefficient; and a high band signal production unit that produces the high band signal of the frame to be processed based on the high band sub-band power and the low band sub-band signal; wherein: the data further includes reuse information indicating whether the coefficient of an initial frame in the section to be processed is the same as the coefficient of a frame just before the initial frame, and when the data includes the reuse information indicating that the coefficients are the same, the data does not include coefficient information of the initial segment of the section to be processed. the data further includes reuse information indicating whether the coefficient of an initial frame in the section to be processed is the same as the coefficient of a frame just before the initial frame, and when the data includes the reuse information indicating that the coefficients are the same, the data does not include coefficient information of the initial segment of the section to be processed.