An FDM system uses single-sideband modulation to combine 12 independent voice signals and then uses frequency modulation to transmit the composite band 0.3 to 3.4 kHz; the system allocates it a bandwidth of 4 kHz. For each voice signal, only the lower sideband is transmitted. The subcarrier waves used for the first stage of modulation are defined by c_k (t) A _k cos (2πkƒ₀t), 0 < k < 11. The received signal consists of the transmitted FM signal plus white Guassian noise of zero mean power spectral density N₀/2.

(a) Sketch the power spectral density of the signal produced at the frequency discriminator output, showing both the signal and noise components.

(b) Find the relationship between the subcarrier amplitudes A _k so that modulated voice signals have equal signal-to-noise ratios.