Bandwidth Bandwidth Bill Joy Category="Filter theory"Category="Information theory"Category="Signal processing"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.

Analog systems

[image] 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 B = 2W, where B is the total bandwidth, and W is the positive bandwidth. For instance, this signal would require a lowpass filter with cutoff frequency of at least W 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
1
–––
√2
 of the maximum signal strength.

In photonics, the term bandwidth occurs in a variety of meanings:

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.

Bandwidth is also used in the sense of Commodity, referring to something limited or something costing money. Thus communication costs bandwidth, and improper use of someone else's web content may be called bandwidth theft.

See also