Bandwidth
From Freepedia
Bandwidth is a measure of frequency range. It is a central concept to many fields including information theory, radio communications, signal processing, and spectroscopy. Bandwidth is closely related to the the capacity of a communications channel: the two are related by Shannon-Hartley theorem. In radio communications, bandwidth is the range of frequencies occupied by a modulated carrier wave, while in optics it is the width of a spectral line or spectral range.
Contents |
Analog systems
For analog signals, which can be mathematically viewed as a function of time, bandwidth is the width, measured in hertz, of a frequency range in which the signal's Fourier transform is nonzero. This definition can be relaxed wherein bandwidth would be the range of frequencies that the signal's Fourier transform has a power above a certain threshold, say 3 dB within the maximum value, in the frequency domain. Intuitively, bandwidth of a signal is a measure of how rapidly it fluctuates with respect to time. Hence, the greater the bandwidth, the faster the variation in the signal.
The fact that real baseband systems have both negative and positive frequencies can lead to confusion about bandwidth, since they are sometimes referred to only by the positive half, and one will occasionally see expressions such as <math>B = 2W</math>, where <math>B</math> is the total bandwidth, and <math>W</math> is the positive bandwidth. For instance, this signal would require a lowpass filter with cutoff frequency of at least <math>W</math> to stay intact.
The bandwidth of an electronic filter is the part of the filter's frequency response that lies within 3 dB of the response at the center frequency of its peak.
In signal processing and control theory the bandwidth is the frequency at which the closed-loop system gain drops to −3 dB.
In basic electric circuit theory when studying Band-pass and Band-reject filters the bandwidth represents the distance between the two points in the frequency domain where the signal is <math>\frac{1}{\sqrt{2}}</math> of the maximum signal strength.
In photonics, the term bandwidth occurs in a variety of meanings:
- the bandwidth of the output of some light source, e.g. an ASE source or a laser; the bandwidth of ultrashort optical pulses can be particularly large
- the width of the frequency range which can be transmitted by some element, e.g. an optical fiber
- the gain bandwidth of an optical amplifier
- the width of the range of some other phenomenon (e.g. a reflection, the phase matching of a nonlinear process, or some resonance)
- the maximum modulation frequency (or range of modulation frequencies) of an optical modulator
- the range of frequencies in which some measurement apparatus (e.g. a powermeter) can operate
- the data rate (e.g. in Gbit/s) achieved in an optical communication system
See also
Digital systems
In a digital communication system, bandwidth has a dual meaning. Technically, it is a synonym for baud rate, the rate at which symbols may be transmitted through the system. It is also used colloquially to describe channel capacity, the rate at which bits may be transmitted through the system. Hence a 66 MHz digital data bus with 32 separate data lines may properly be said to have a bandwidth of 66 MHz and a capacity of 2.1 Gbit/s — but it would not be surprising to hear such a bus described as a having a "bandwidth of 2.1 Gbit/s". Similar confusion exists for analog modems, where each symbol carries multiple bits of information so that an modem may transmit 56 kbit/s of information over a phone line with a bandwidth of only 12 kHz.
In discrete time systems and digital signal processing, bandwidth is related to sampling rate according to the Nyquist-Shannon sampling theorem.
See also
- Shannon–Hartley theorem
- List of device bandwidths
- Latency vs Bandwidth
- Bandwidth theft
- Bandwidth cap
- Throughput
- Measuring data throughput
- Bandwidth Controller
- Data rate
