An encoder comprising: a first encoding unit that encodes a low-band signal having a frequency lower than or equal to a predetermined frequency from a voice or audio input signal to generate a first encoded signal, and decodes the first encoded signal to generate a low-band decoded signal; a second encoding unit that encodes, on the basis of the low-band decoded signal, a high-band signal from the voice or audio input signal having a band higher than that of the low-band signal to generate a high-band encoded signal, wherein the second encoding unit comprises: a separating unit that separates, from the low-band decoded signal, a low-band noise signal, which is a noise component of the low-band decoded signal, and a low-band tonal signal, which is a tonal component of the low-band decoded signal, a first bandwidth extending unit that outputs, as a lag information, a position information regarding a specific band in which a correlation between the high-band signal and the low-band tonal signal becomes maximum, a second bandwidth extending unit that outputs, as a high-band noise signal, the low-band noise signal corresponding to the lag information, a first calculating unit that calculates an energy of the high-band noise component from the high-band signal using the lag information, a second calculating unit that calculates an energy of the high-band noise signal, that calculates a ratio between the energy of the high-band noise component and the energy of the high-band noise signal, and that outputs the calculated ratio as a scaling factor; an energy calculating unit that calculates an energy of the voice or audio input signal and outputs the calculated energy as a quantized band energy; and a multiplexing unit (103, 207) that multiplexes the first encoded signal, the quantized band energy, and the lag information and the scaling factor as the high-band encoded signal to generate and output an encoded signal. a first encoding unit that encodes a low-band signal having a frequency lower than or equal to a predetermined frequency from a voice or audio input signal to generate a first encoded signal, and decodes the first encoded signal to generate a low-band decoded signal; a second encoding unit that encodes, on the basis of the low-band decoded signal, a high-band signal from the voice or audio input signal having a band higher than that of the low-band signal to generate a high-band encoded signal, wherein the second encoding unit comprises: a separating unit that separates, from the low-band decoded signal, a low-band noise signal, which is a noise component of the low-band decoded signal, and a low-band tonal signal, which is a tonal component of the low-band decoded signal, a first bandwidth extending unit that outputs, as a lag information, a position information regarding a specific band in which a correlation between the high-band signal and the low-band tonal signal becomes maximum, a second bandwidth extending unit that outputs, as a high-band noise signal, the low-band noise signal corresponding to the lag information, a first calculating unit that calculates an energy of the high-band noise component from the high-band signal using the lag information, a second calculating unit that calculates an energy of the high-band noise signal, that calculates a ratio between the energy of the high-band noise component and the energy of the high-band noise signal, and that outputs the calculated ratio as a scaling factor; a separating unit that separates, from the low-band decoded signal, a low-band noise signal, which is a noise component of the low-band decoded signal, and a low-band tonal signal, which is a tonal component of the low-band decoded signal, a first bandwidth extending unit that outputs, as a lag information, a position information regarding a specific band in which a correlation between the high-band signal and the low-band tonal signal becomes maximum, a second bandwidth extending unit that outputs, as a high-band noise signal, the low-band noise signal corresponding to the lag information, a first calculating unit that calculates an energy of the high-band noise component from the high-band signal using the lag information, a second calculating unit that calculates an energy of the high-band noise signal, that calculates a ratio between the energy of the high-band noise component and the energy of the high-band noise signal, and that outputs the calculated ratio as a scaling factor; an energy calculating unit that calculates an energy of the voice or audio input signal and outputs the calculated energy as a quantized band energy; and a multiplexing unit (103, 207) that multiplexes the first encoded signal, the quantized band energy, and the lag information and the scaling factor as the high-band encoded signal to generate and output an encoded signal.