In an FDM communication system, the transmitted base band signal is x(t) = m 1 (t) cos(2f

In an FDM communication system, the transmitted base band signal is

x(t) = m₁(t) cos(2πf₁t) + m₂(t) cos(2πf₂t)

This system has a second-order non-linearity between transmitter output and receiver input. Thus, the received base band signal y(t) can be expressed as 

y(t) = a₁x(t) + a₂x²(t)

Assuming that the two message signals, m₁ (t) and m₂ (t), have the spectra

M₁(f) = M₂ (f) = II(f / w)

sketch the spectrum of y(t) Discuss the difficulties encountered in demodulating the received base band signal. In many FDM systems, the sub-carrier frequencies f₁ and f₂ are harmonically related. Describe any additional problems this presents.