Frequency modulation and phase modulation are physically equivalent.

Edit conflict - other version:

Suppose you have unmodulated sinusoidal signal, e^{w t}

This signal has the phase of phi(t) = w t, and frequency of f(t) = 1/(2 pi) * dphi/dt = w/(2 pi) = f0.

Edit conflict - your version:

Suppose you have unmodulated sinusoidal signal, e^{w t}

This signal has the phase of

• phi(t) = w t,

and frequency of

• f(t) = 1/(2 pi) * dphi/dt = w/(2 pi) = f0.

End of edit conflict

Now we apply the frequency modulation with frequency deviation of df and modulation frequency of fm:

• f(t) = f0 + df Cos(2 pi fm t)

• phi(t) = Integrate[f(t) dt] = w t + df/fm * Sin(2 pi fm t)

Now think about the phase modulation with modulation depth of m and modulation frequency of fm:

This means that the effect of FM is the same as that of PM. This indicates that the modulation depth of FM is given by m = df / fm. For given df, FM gives a larger modulation depth with a lower modulation frequency.