An AM signal has the form: \[ s(t)=5 \cos (1800 \pi t)+20 \cos (2000 \pi t)+5 \cos (2200 \pi t) \] (a) Determine the modulating signal \( m(t) \) and the carrier \( c(t) \). (b) Determine the Fourier transform of s(t) and plot its amplitude spectrum. (c) Determine its modulation index. (d) Determine the ratio of the power in the sidebands to the power in the carrier.