Let  and  it is given that  The signal  is applied to the input of a non-linear device, whose output  is related to the input  as  where  and  are positive constants. The output of the non-linear device is passed through an ideal band-pass filter with center frequency  and bandwidth  to produce an amplitude modulated (AM) wave. If it is desired to have the sideband power of the AM wave to be half of the carrier power, then  is