Theory
If the baseband data signal (the message) to be transmitted is and the sinusoidal carrier is, where fc is the carrier's base frequency and Ac is the carrier's amplitude, the modulator combines the carrier with the baseband data signal to get the transmitted signal:
In this equation, is the instantaneous frequency of the oscillator and is the frequency deviation, which represents the maximum shift away from fc in one direction, assuming xm(t) is limited to the range ±1.
While most of the energy of the signal is contained within fc ± fΔ, it can be shown by Fourier analysis that a wider range of frequencies is required to precisely represent an FM signal. The frequency spectrum of an actual FM signal has components extending infinitely, although their amplitude decreases and higher-order components are often neglected in practical design problems.
Read more about this topic: Frequency Modulation
Famous quotes containing the word theory:
“Freud was a hero. He descended to the “Underworld” and met there stark terrors. He carried with him his theory as a Medusa’s head which turned these terrors to stone.”
—R.D. (Ronald David)
“By the “mud-sill” theory it is assumed that labor and education are incompatible; and any practical combination of them impossible. According to that theory, a blind horse upon a tread-mill, is a perfect illustration of what a laborer should be—all the better for being blind, that he could not tread out of place, or kick understandingly.... Free labor insists on universal education.”
—Abraham Lincoln (1809–1865)
“It makes no sense to say what the objects of a theory are,
beyond saying how to interpret or reinterpret that theory in another.”
—Willard Van Orman Quine (b. 1908)