A bandwidth extension decoder (500), (600) for providing a bandwidth extended audio signal (532) based on an input audio signal (502) and a parameter signal (504), wherein the parameter signal (504) comprises an indication of an offset frequency and an indication of a power density parameter, comprises: a patch generator (510) configured to generate a bandwidth extension high-frequency signal (512) comprising a high-frequency band, wherein the high-frequency band of the bandwidth extension high-frequency signal (512) is generated based on a frequency shift of a frequency band of the input audio signal (502), wherein the frequency shift is based on the offset frequency, and wherein the patch generator (510) is configured to amplify or attenuate the high-frequency band of the bandwidth extension high-frequency signal (512) by a factor equal to the value of the power density parameter or equal to the reciprocal value of the power density parameter, respectively; a combiner (529) configured to combine the bandwidth extension high-frequency signal (512) and the input audio signal (502) to obtain the bandwidth extended audio signal (532); and an output interface (530) configured to provide the bandwidth extended audio signal (532) .