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← Revision 6 as of 2012-01-03 23:02:40 ⇥
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---- /!\ '''Edit conflict - other version:''' ---- |
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| This signal has the phase of phi(t) = w t, and frequency of f(t) = 1/(2 pi) * dphi/dt = w/(2 pi) = f0. | This signal has the phase of |
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| ---- /!\ '''Edit conflict - your version:''' ---- Suppose you have unmodulated sinusoidal signal, '''e^w t^''' |
. '''phi(t) = w t,''' |
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| This signal has the phase of . '''phi(t) = w t,''' and frequency of |
and frequency of |
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| ---- /!\ '''End of edit conflict''' ---- Now we apply the frequency modulation with frequency deviation of df and modulation frequency of fm: |
Now we apply the frequency modulation with frequency deviation of df and modulation frequency of fm: |
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| 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'''. |
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'''. |
Frequency modulation and phase modulation are physically equivalent.
Suppose you have unmodulated sinusoidal signal, ew 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.
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.