Editing Frequency modulation (section)

===Modulation index===
As in other modulation systems, the modulation index indicates by how much the modulated variable varies around its unmodulated level. It relates to variations in the [[carrier frequency]]:

:<math>h = \frac{\Delta{}f}{f_m} = \frac{f_\Delta \left|x_m(t)\right|}{f_m}</math>

where <math>f_m\,</math> is the highest frequency component present in the modulating signal ''x''<sub>''m''</sub>(''t''), and <math>\Delta{}f\,</math> is the peak frequency-deviation{{snd}}i.e. the maximum deviation of the ''[[instantaneous phase#Instantaneous frequency|instantaneous frequency]]'' from the carrier frequency. For a sine wave modulation, the modulation index is seen to be the ratio of the peak frequency deviation of the carrier wave to the frequency of the modulating sine wave.

{{anchor|narrowband_FM_anchor}}If <math>h \ll 1</math>, the modulation is called '''narrowband FM''' (NFM), and its bandwidth is approximately <math>2f_m\,</math>. Sometimes modulation index <math>h < 0.3</math>&nbsp;is considered NFM and other modulation indices are considered wideband FM (WFM or FM).

For digital modulation systems, for example, binary frequency shift keying (BFSK), where a binary signal modulates the carrier, the modulation index is given by:

:<math>h = \frac{\Delta{}f}{f_m} = \frac{\Delta{}f}{\frac{1}{2T_s}} = 2\Delta{}fT_s \ </math>

where <math>T_s\,</math> is the symbol period, and <math>f_m = \frac{1}{2T_s}\,</math> is used as the highest frequency of the modulating binary waveform by convention, even though it would be more accurate to say it is the highest ''fundamental'' of the modulating binary waveform. In the case of digital modulation, the carrier <math>f_c\,</math> is never transmitted. Rather, one of two frequencies is transmitted, either <math>f_c + \Delta f</math> or <math>f_c - \Delta f</math>, depending on the binary state 0 or 1 of the modulation signal.

If <math>h \gg 1</math>, the modulation is called ''wideband FM'' and its bandwidth is approximately <math>2f_\Delta\,</math>. While wideband FM uses more bandwidth, it can improve the [[signal-to-noise ratio]] significantly; for example, doubling the value of <math>\Delta{}f\,</math>, while keeping <math>f_m</math> constant, results in an eight-fold improvement in the signal-to-noise ratio.<ref>{{cite web |last=Der |first=Lawrence |title=Frequency Modulation (FM) Tutorial |url=http://www.silabs.com/Marcom%20Documents/Resources/FMTutorial.pdf |archive-url=https://web.archive.org/web/20141021093250/http://www.silabs.com/Marcom%20Documents/Resources/FMTutorial.pdf |archive-date=2014-10-21 |website=Silicon Laboratories |s2cid=48672999 |access-date=17 October 2019}}</ref> (Compare this with [[chirp spread spectrum]], which uses extremely wide frequency deviations to achieve processing gains comparable to traditional, better-known spread-spectrum modes).

With a tone-modulated FM&nbsp;wave, if the modulation frequency is held constant and the modulation index is increased, the (non-negligible) bandwidth of the FM signal increases but the spacing between spectra remains the same; some spectral components decrease in strength as others increase. If the frequency deviation is held constant and the modulation frequency increased, the spacing between spectra increases.

{{anchor|narrowband FM}}
Frequency modulation can be classified as narrowband if the change in the carrier frequency is about the same as the signal frequency, or as wideband if the change in the carrier frequency is much higher (modulation index&nbsp;>&nbsp;1) than the signal frequency.<ref>Lathi, B. P. (1968). ''Communication Systems'', pp.&nbsp;214–17. New York: John Wiley and Sons, {{ISBN|0-471-51832-8}}.</ref> For example, narrowband FM (NFM) is used for [[two-way radio]] systems such as [[Family Radio Service]], in which the carrier is allowed to deviate only 2.5&nbsp;kHz above and below the center frequency with speech signals of no more than 3.5&nbsp;kHz bandwidth. Wideband FM is used for [[FM broadcasting]], in which music and speech are transmitted with up to 75&nbsp;kHz deviation from the center frequency and carry audio with up to a 20&nbsp;kHz bandwidth and subcarriers up to 92&nbsp;kHz.