In a single-tone AM, message signal is a single-tone being modulated by a carrier signal and generates a single-tone modulated signal, where as in Multi-tone environment message signal is a composite signal formed by number of frequencies f1,f2,f3 …..fn … being modulated by a carrier signal to generate an Amplitude Modulated signal.
i.e, Multi-tone message signal is
Now from the equation of General AM signal
the Multi-tone modulated signal can be obtained as
from the above signal the total power can be obtained as
This expression can further represented in terms of effective modulation index as where