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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
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}\,} .
Carrier wave - Wikipedia
Waterfall plot of a 146.52 MHz radio carrier, with amplitude modulation by a 1,000 Hz sinusoid. Two strong sidebands at + and - 1 kHz from the carrier frequency are shown. A carrier, frequency modulated by a 1,000 Hz sinusoid. The modulation index has been adjusted to around 2.4, so the carrier frequency has small amplitude. Several strong ...
Consequently, the waveforms that represent a 0 and a 1 bit differ by exactly half a carrier period. The maximum frequency deviation is δ = 0.25 f m, where f m is the maximum modulating frequency. As a result, the modulation index m is 0.5. This is the smallest FSK modulation index that can be chosen such that the waveforms for 0 and 1 are ...
A diagram with four points, for example, represents a modulation scheme that can separately encode all 4 combinations of two bits: 00, 01, 10, and 11, and so can transmit two bits per sample. Thus in general a modulation with N {\displaystyle N} constellation points transmits log 2 N {\displaystyle \log _{2}N} bits per sample.
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.
Example (chirped pulse): transmitted signal in red (carrier 10 hertz, modulation on 16 hertz, amplitude 1, duration 1 second) and two echoes (in blue). Before matched filtering: the echoes are long and have a low amplitude: After matched filtering: the echoes are shorter in time and have a higher peak power.