An FDM communication system uses DSB modulation to form the base band and FM modulation for transmission of the base band. Assume that there are eight channels and that all eight message signals have equal power P₀ and equal bandwidth W. One channel does not use sub carrier modulation. The other channels use sub carriers of the form 

A_k cos (2πkf₁t),    1 ≤ k ≤ 7

The width of the guard bands is 3W. Sketch the power spectrum of the received base band signal showing both the signal and noise components. Calculate the relationship between the values of A_k if the channels are to have equal SNRs.