Diff for "FMandPM"

Differences between revisions 1 and 6 (spanning 5 versions)

Frequency modulation and phase modulation are physically equivalent.

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

This signal has the phase of

and frequency of

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

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

For given df, FM gives a larger modulation depth with a lower modulation frequency.

-  ⇤ ← Revision 1 as of 2010-11-04 02:53:02 → 
  Size: 757
  Editor: KojiArai
  Comment:
+   ← Revision 6 as of 2012-01-03 23:02:40 → ⇥
  Size: 817
  Editor: localhost
  Comment: converted to 1.6 markup
-Deletions are marked like this.
+Additions are marked like this.
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-Suppose you have unmodulated sinusoidal signal, e^w t^
+Suppose you have unmodulated sinusoidal signal, '''e^w t^'''
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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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-Now we apply the frequency modulation with frequency deviation of df and modulation frequency of fm:
+ . '''phi(t) = w t,'''
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- . f(t) = f0 + df Cos(2 pi fm t)
 . phi(t) = Integrate[f(t) dt] = w t + df/fm * Sin(2 pi fm 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)'''
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+Line 20:
-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'''.