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The Rayleigh bandwidth of a simple radar pulse is defined as the inverse of its duration. For example, a one-microsecond pulse has a Rayleigh bandwidth of one megahertz. [1] The essential bandwidth is defined as the portion of a signal spectrum in the frequency domain which contains most of the energy of the signal. [2]
At a SNR of 0 dB (Signal power = Noise power) the Capacity in bits/s is equal to the bandwidth in hertz. If the SNR is 20 dB, and the bandwidth available is 4 kHz, which is appropriate for telephone communications, then C = 4000 log 2 (1 + 100) = 4000 log 2 (101) = 26.63 kbit/s. Note that the value of S/N = 100 is equivalent to the SNR of 20 dB.
The consumed bandwidth in bit/s, corresponds to achieved throughput or goodput, i.e., the average rate of successful data transfer through a communication path.The consumed bandwidth can be affected by technologies such as bandwidth shaping, bandwidth management, bandwidth throttling, bandwidth cap, bandwidth allocation (for example bandwidth allocation protocol and dynamic bandwidth ...
In the late 1990s, this work was partially extended to cover signals for which the amount of occupied bandwidth is known but the actual occupied portion of the spectrum is unknown. [7] In the 2000s, a complete theory was developed (see the section Sampling below the Nyquist rate under additional restrictions below) using compressed sensing .
The convention of "width" meaning "half maximum" is also widely used in signal processing to define bandwidth as "width of frequency range where less than half the signal's power is attenuated", i.e., the power is at least half the maximum.
Fig 1: Typical example of Nyquist frequency and rate. They are rarely equal, because that would require over-sampling by a factor of 2 (i.e. 4 times the bandwidth). In signal processing, the Nyquist rate, named after Harry Nyquist, is a value equal to twice the highest frequency of a given function or signal.
Two examples show the spectra of linear chirps with finite rise-times. The first is for a chirp with time-bandwidth of 250, where the rise and fall times are 4% of the total pulse duration and the second is for a chirp with time-bandwidth of 25, where the rise and fall times are 10% of the total.
This is called the bandwidth-limited regime. When the SNR is small (SNR ≪ 0 dB), the capacity ¯ is linear in power but insensitive to bandwidth. This is called the power-limited regime. The bandwidth-limited regime and power-limited regime are illustrated in the figure.