Frequency Modulation 4; Other Types of FM. “Normal” Single-Modulator FM. Frequency Modulation M odulation in frequency. x(t) = w(t)sin[2 (f c + If m sin(2 f m t))t]. Phase Modulation. Phase Modulation Equivalent to FM – implements the modulation in the phase instead of frequency.
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Other Types of FM
Modulation in frequency.
x(t) = w(t)sin[2(fc + Ifmsin(2fmt))t]
Equivalent to FM – implements the modulation in the phase instead of frequency.
x(t) = w(t)sin[2fct + Isin(2fmt)]
Uses two parallel modulators.
x(t) = w(t) sin[2fct
[J(k-nc-hnm)(Im1) - J- (k+nc+hnm)(Im1)] Jh(Im2)
Uses nested (serial) modulators.
x(t) = w(t)sin[2fct+
Im1sin(2fm1t + Im2sin(2fm2t))]
Nested FM is more nonlinear than double FM, making optimization more difficult.
A discrete formula for feedback FM is the following:
xn = wnsin[(2f1n/SR) + (Bxn-1/wn-1)]
with wn the discrete carrier amplitude envelope, and f1 the desired fundamental frequency.
FM with 3 nested modulators is best for a fixed number of carriers.
FeedbackFM is bestfor a fixed number of table lookups (computations)