A signal processing device, comprising: a frequency detecting means configured to: calculate a level of a first frequency region in the audio signal and a level of a second frequency region higher than the first frequency region in the audio signal, set a threshold based on the calculated levels of the first frequency region and the second frequency region, and detect a frequency of which level is lower than a level of the set threshold; an offset means configured to: detect a changing rate of level of the audio signal at the detected frequency or around the detected frequency, change an offset amount for the detected frequency so as to set the offset amount to become larger as said changing rate becomes smaller, and give an offset to the detected frequency by the frequency detecting means by the set offset amount; a reference signal generating means configured to extract, from the audio signal, a signal corresponding to a range extending from the detected frequency offset by the offset means by n% toward a lower frequency side, and generate a reference signal using the extracted signal; an interpolation signal generating means configured to generate an interpolation signal based on the generated reference signal; and a signal synthesizing means configured to high band interpolation by synthesizing the generated interpolation signal and the audio signal. a frequency detecting means configured to: calculate a level of a first frequency region in the audio signal and a level of a second frequency region higher than the first frequency region in the audio signal, set a threshold based on the calculated levels of the first frequency region and the second frequency region, and detect a frequency of which level is lower than a level of the set threshold; calculate a level of a first frequency region in the audio signal and a level of a second frequency region higher than the first frequency region in the audio signal, set a threshold based on the calculated levels of the first frequency region and the second frequency region, and detect a frequency of which level is lower than a level of the set threshold; an offset means configured to: detect a changing rate of level of the audio signal at the detected frequency or around the detected frequency, change an offset amount for the detected frequency so as to set the offset amount to become larger as said changing rate becomes smaller, and give an offset to the detected frequency by the frequency detecting means by the set offset amount; a reference signal generating means configured to extract, from the audio signal, a signal corresponding to a range extending from the detected frequency offset by the offset means by n% toward a lower frequency side, and generate a reference signal using the extracted signal; an interpolation signal generating means configured to generate an interpolation signal based on the generated reference signal; and a signal synthesizing means configured to high band interpolation by synthesizing the generated interpolation signal and the audio signal. detect a changing rate of level of the audio signal at the detected frequency or around the detected frequency, change an offset amount for the detected frequency so as to set the offset amount to become larger as said changing rate becomes smaller, and give an offset to the detected frequency by the frequency detecting means by the set offset amount; a reference signal generating means configured to extract, from the audio signal, a signal corresponding to a range extending from the detected frequency offset by the offset means by n% toward a lower frequency side, and generate a reference signal using the extracted signal; an interpolation signal generating means configured to generate an interpolation signal based on the generated reference signal; and a signal synthesizing means configured to high band interpolation by synthesizing the generated interpolation signal and the audio signal.