Bandwidth extension decoder (500, 600) for providing a bandwidth extended audio signal based on an input audio signal and a parameter signal, wherein the parameter signal comprises an indication of an offset frequency and an indication of a power density parameter, the bandwidth extension decoder comprising: a patch generator configured to generate a bandwidth extension high-frequency signal comprising a high-frequency band, wherein the high-frequency band of the bandwidth extension high-frequency signal is generated by performing a frequency shift of a frequency band of the input audio signal to higher frequencies, wherein the frequency shift is based on the offset frequency, and wherein the patch generator is configured to amplify or attenuate the high-frequency band of the bandwidth extension high-frequency signal 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 configured to combine the bandwidth extension high-frequency signal and the input audio signal to obtain the bandwidth extended audio signal; an output interface configured to provide the bandwidth extended audio signal; and a core decoder and a parameter extraction unit, wherein the core decoder is connected to the patch generator and the combiner, wherein the parameter extraction unit is connected to the patch generator and to the output interface, wherein the patch generator is connected to the combiner, wherein the combiner is connected to the output interface, wherein the parameter extraction unit is configured to separate the parameter signal from a received bit stream and to provide the parameter signal to the patch generator, and preferably to provide the parameter signal or an extracted noise and/or tonality parameter to the output interface. a patch generator configured to generate a bandwidth extension high-frequency signal comprising a high-frequency band, wherein the high-frequency band of the bandwidth extension high-frequency signal is generated by performing a frequency shift of a frequency band of the input audio signal to higher frequencies, wherein the frequency shift is based on the offset frequency, and wherein the patch generator is configured to amplify or attenuate the high-frequency band of the bandwidth extension high-frequency signal 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 configured to combine the bandwidth extension high-frequency signal and the input audio signal to obtain the bandwidth extended audio signal; an output interface configured to provide the bandwidth extended audio signal; and a core decoder and a parameter extraction unit, wherein the core decoder is connected to the patch generator and the combiner, wherein the parameter extraction unit is connected to the patch generator and to the output interface, wherein the patch generator is connected to the combiner, wherein the combiner is connected to the output interface, wherein the parameter extraction unit is configured to separate the parameter signal from a received bit stream and to provide the parameter signal to the patch generator, and preferably to provide the parameter signal or an extracted noise and/or tonality parameter to the output interface.