The square-law modulator is a device for the generation of DSB-PC-AM signals. In the square-law modulator, the sum of the modulating signal and the carrier wave forms the input signal to a nonlinear device. The output signal of the nonlinear device is a linear combination of the input signal and the square of the input signal. The output signal of the nonlinear device is then band-pass filtered. The BPF has a center frequency that is the same as the carrier frequency and a bandwidth that is twice the message bandwidth. Show the output of the BPF is a DSB-PC-AM signal, and determine a requirement between the carrier frequency and the message bandwidth that must be satisfied.