Frequency modulation (FM) is variation of the frequency of a carrier wave,commonly a radio wave in accordance with variations in the audio signal being sent. Developed by American electrical engineer Edwin H. Armstrong in the early 1930s, FM is less susceptible to outside interference and noise example of FM such as thunderstorms and nearby machinery. Such noise generally affects the amplitude of a radio wave but not its frequency, so an FM signal remains virtually unchanged. FM is also better able to transmit sounds in stereo than AM. Commercial FM broadcasting stations transmit their signals in the frequency range of 88 megahertz (MHz) to 108 MHz.Analog applications, the difference between the instantaneous and the base frequency of the carrier is directly proportional to the instantaneous value of the input signal amplitude. Digital data can be sent by shifting the carrier's frequency among a set of discrete values, a technique known as frequency-shift keying. Frequency modulation can be regarded as phase modulation where the carrier phase modulation is the time integral of the FM modulating signal.FM is widely used for broadcasting of music and speech, and in two-way radio systems, in magnetic tape recording systems, and certain video transmission systems. In radio systems, frequency modulation with sufficient bandwidth provides an advantage in cancelling naturally-occurring noise.

Frequency spectrum of an FM wave
The spectrum of an FM wave is complex mathematically. It consists of a carrier wave with a (theoretically infinite) series of pairs of sidebands. The amplitude of the carrier and each pair of sidebands is given by Bessel functions. Bessel function values for the carrier and first 5 sidebands (but realise that it is an infinite series of sidebands. the amplitude of the higher sidebands is very low at low modulation indexes and can be ignored).

Carson's rule
Carson's rule is often used to estimate the occupied bandwidth of an FM signal. Carson's rule estimates the bandwidth as twice the sum of the peak deviation and the highest modulating frequency.
BW=2×(D_max+ F_(max ))
Dmax = peak frequency deviation
Fmax = highest modulating frequency

There are many applications that use fm frequency as their signal. One of it is fm radio. As the name implies, wideband FM (WFM) requires a wider signal bandwidth than amplitude modulation by an equivalent modulating signal, but this also makes the signal more robust against noise and interference. Frequency modulation is also more robust against simple signal amplitude fading phenomena. As a result, FM was chosen as the modulation standard for high frequency, high fidelity radio transmission: hence the term "FM radio" (although for many years the BBC called it "VHF radio", because commercial FM broadcasting uses a well-known part of the VHF band-the FM broadcast band).FM receivers employ a special detector for FM signals and exhibit a phenomenon called capture effect, where the tuner is able to clearly receive the stronger of two stations being broadcast on the same frequency. Problematically however, frequency drift or lack of selectivity may cause one station or signal to be suddenly overtaken by another on an adjacent channel. Frequency drift typically constituted a problem on very old or inexpensive receivers, while inadequate selectivity may plague any tuner. An FM signal can also be used to carry a stereo signal: see FM stereo. However, this is done by using multiplexing and demultiplexing before and after the FM process. The rest of this article ignores the stereo multiplexing and demultiplexing process used in "stereo FM", and concentrates on the FM modulation and demodulation process, which is identical in stereo and mono processes. A high-efficiency radio-frequency switching amplifier can be used to transmit FM signals (and other constant-amplitude signals). For a given signal strength (measured at the receiver antenna), switching amplifiers use less battery power and typically cost less than a linear amplifier. This gives FM another advantage over other modulation schemes that require linear amplifiers, such as AM and QAM.FM is commonly used at VHF radio frequencies for high-fidelity broadcasts of music and speech (see FM broadcasting). Normal (analog) TV sound is also broadcast using FM. A narrow band form is used for voice communications in commercial and amateur radio settings.

In AM or Amplitude Modulation, the information is added to the amplitude of the carrier signal. When your receiver receives the signal, it does an analog sample of the wave to determine it's average strength, then demodulates the differences in the amplitude to pull out the original information. This is the worst and most inaccurate way of demodulation, for the signal strength is continuously changing, with the analog demodulator always working "behind the times". This is why it took so many years for the occurrence of AM Stereo. It's hard enough to accurately pull one stream of info out of the carrier wave. Try pulling two distinct signals out of one carrier wave that is Amplitude modulated. How in the world do you do that??? (But they do have AM stereo now, yet not very popular) The reason it came first, is it is very easy to mix amplitudes, and no complicated circuitry was required in the old days to pull in the correct carrier wave. They couldn't do frequency modulation at first cause uncle sam wouldn't let commercial businesses transmit on high enough frequencies to pull out the original information. Also since AM carrier waves have relatively low frequencies, they can travel quite a distance.

In Frequency Modulation, the information is added to the frequency of the carrier wave. The amplitude of the incoming signal is a mute point as long as it is strong enough where your receiver can lock onto the carrier wave. Carrier frequencies in high ranges were released for commercial use, so they could transmit in the Megahertz range. Since all information needed in the hearing range is commonly in the 20 to 20KiloHertz range, it was easy to pull the signal in. The information didn't cause enough of a difference in the signal to cause the tuner to filter it out. And since the original carrier frequency is known, and locked in, it was extremely easy to pull out the original information. In fact, you could add 6 or 8 different information signals if you wanted to. Complex, but achievable. Since the demodulation is so accurate, this gives it better clarity, and the ability to modulate 2 separate signals for stereo. However, since the carrier frequency is so high, it bounces off obstacles instead of going through them, thus reducing range.