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:
“every subjective phenomenon is essentially connected with a single point of view, and it seems inevitable that an objective, physical theory will abandon that point of view.”
—Thomas Nagel (b. 1938)
“In the theory of gender I began from zero. There is no masculine power or privilege I did not covet. But slowly, step by step, decade by decade, I was forced to acknowledge that even a woman of abnormal will cannot escape her hormonal identity.”
—Camille Paglia (b. 1947)
“The theory of the Communists may be summed up in the single sentence: Abolition of private property.”
—Karl Marx (1818–1883)