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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. If h ≪ 1 {\displaystyle h\ll 1} , the modulation is called narrowband FM (NFM), and its bandwidth is approximately 2 f m {\displaystyle 2f_{m}\,} .
The modulation index (or modulation depth) of a modulation scheme describes by how much the modulated variable of the carrier signal varies around its unmodulated level. It is defined differently in each modulation scheme. Amplitude modulation index; Frequency modulation index; Phase modulation index
However, many modulation schemes make this simple approach impractical because most signal power is devoted to modulation—where the information is present—and not to the carrier frequency. Reducing the carrier power results in greater transmitter efficiency. Different methods must be employed to recover the carrier in these conditions.
The frequency spectrum of a typical radio signal from an AM or FM radio transmitter. The horizontal axis is frequency; the vertical axis is signal amplitude or power. It consists of a signal (C) at the carrier wave frequency f C, with the modulation contained in narrow frequency bands called sidebands (SB) just above and below the carrier.
Note that since this resultant wave is continuously phase shifting at a steady rate, effectively the frequency has been changed: it has been frequency modulated. And if the IQ data itself has some frequency (e.g. a phasor) then the carrier also can be frequency modulated. So I/Q data is a complete representation of how a carrier is modulated ...
A 220 Hz carrier tone f c modulated by a 440 Hz modulating tone f m, with various choices of frequency modulation index, β. The time domain signals are illustrated above, and the corresponding spectra are shown below (spectrum amplitudes in dB). Waveforms for each β. Spectra for each β
To sufficiently attenuate the frequency of the carrier wave frequency , the cutoff frequency of the low-pass filter should be well-below the carrier wave's frequency. To avoid negative peak clipping, the original signal that is modulated is usually limited to a maximum frequency f max {\displaystyle f_{\text{max}}} to limit the maximum rate of ...
is the peak frequency deviation; is the highest frequency in the modulating signal. For example, a typical VHF/UHF two-way radio signal using FM mode, [2] with 5 kHz peak deviation, and a maximum audio frequency of 3 kHz, would require an approximate bandwidth of 2 × (5 kHz + 3 kHz) = 16 kHz.