Diff for "FMandPM"

Differences between revisions 2 and 4 (spanning 2 versions)

Frequency modulation and phase modulation are physically equivalent.

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.

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.

-  ⇤ ← Revision 2 as of 2010-11-04 02:55:05 → 
  Size: 763
  Editor: KojiArai
  Comment:
+   ← Revision 4 as of 2010-11-04 02:57:18 → ⇥
  Size: 807
  Editor: KojiArai
  Comment:
-Deletions are marked like this.
+Additions are marked like this.
 Line 5:
-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
 Line 7:
-Now we apply the frequency modulation with frequency deviation of df and modulation frequency of fm:
+ . '''phi(t) = w t,'''
 Line 9:
- . 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)'''
-Line 14:
+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.
For given df, FM gives a larger modulation depth with a lower modulation frequency.
+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.