Bandwidth explained

Bandwidth is the difference between the upper and lower cutoff frequencies of for example a filter, a communication channel or a signal spectrum, and is typically measured in hertz. Bandwidth in Hertz is a central concept in many fields, including electronics, information theory, radio communications, signal processing, and spectroscopy.

In computer networking literature, digital bandwidth often refers to data rate measured in bit/s, for example channel capacity (digital bandwidth capacity) or throughput (digital bandwidth consumption). The reason for this usage is that the channel capacity in bit/s is proportional to the analogue bandwidth in Hertz according to Hartley's law.

Meaning of bandwidth in web hosting

In website hosting, the term "bandwidth" is often used metaphorically, to describe the amount of data that can be transferred to or from the website or server, measured in bytes transferred over a prescribed period of time. This can be more accurately described as "Monthly Data Transfer."

Web hosting companies often quote a monthly bandwidth limit for a website, for example 500 gigabytes per month. If visitors to the website download a total greater than 500 gigabytes in one month, the bandwidth limit will have been exceeded, however, on best web hosting providers such practices are not used!

Overview

Bandwidth is a key concept in many applications. In radio communications, for example, bandwidth is the range of frequencies occupied by a modulated carrier wave, whereas in optics it is the width of an individual spectral line or the entire spectral range.

There is no single universal precise definition of bandwidth, as it is vaguely understood to be a measure of how wide a function is in the frequency domain.

For different applications there are different precise definitions. For example, one definition of bandwidth could be the range of frequencies beyond which the frequency function is zero. This would correspond to the mathematical notion of the support of a function (i.e., the total "length" of values for which the function is nonzero). A less strict and more practically useful definition will refer to the frequencies where the frequency function is small. Small could mean less than 3 dB below (i.e., less than half of) the maximum value, or more rarely 10 dB, or it could mean below a certain absolute value. As with any definition of the width of a function, many definitions are suitable for different purposes.

According to the Shannon-Hartley theorem, the data rate of reliable communication is directly proportional to the frequency range of the signal used for the communication. In this context, the word bandwidth can refer to either the data rate or the frequency range of the communication system (or both).

Analog systems

For analog signals, which can be mathematically viewed as functions of time, bandwidth is the width, measured in hertz, of the frequency range in which the signal's Fourier transform is nonzero. Because this range of non-zero amplitude may be very broad, this definition is often relaxed so that the bandwidth is defined as the range of frequencies where the signal's Fourier transform has a power above a certain amplitude threshold, commonly half the maximum value. Bandwidth of a signal is a measure of how rapidly its parameters (e.g. amplitude and phase) fluctuate with respect to time. Hence, the greater the bandwidth, the faster the variation in the signal parameters may be. The wordbandwidth applies to signals as described above, but it could also apply to systems. In the latter case, to say that a system has a certain bandwidth means that the system can process signals of that bandwidth.

A baseband bandwidth is a specification of only the highest frequency limit of a signal. A non-baseband bandwidth is a difference between highest and lowest frequencies.

A commonly used quantity is fractional bandwidth. This is the bandwidth of a device divided by its center frequency. E.g., a device that has a bandwidth of 2 MHz with center frequency 10 MHz will have a fractional bandwidth of 2/10, or 20%.

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 3-dB bandwidth of an electronic filter is the part of the filter's frequency response that lies within 3 dB of the response at its peak, which is typically at or near its center frequency.

In signal processing and control theory the bandwidth is the frequency at which the closed-loop system gain drops 3 dB below peak.

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 that 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

Digital systems

When used to discuss digital communication, the meaning of "bandwidth" is clouded by metaphorical use. Technicians sometimes use it as slang for Baud, the rate at which symbols may be transmitted through the system. It is also used more colloquially to describe channel capacity, the rate at which bits may be transmitted through the system (see Shannon Limit). Hence, a digital data bus with a bit rate of 66 Mbit/s on each of 32 separate data lines may properly be said to have a bandwidth of 33 MHz and a capacity of 2.1 Gbit/s - but it would not be surprising to hear such a bus described as having a "bandwidth of 2.1 Gbit/s." Similar confusion exists for voiceband modems, where each symbol carries multiple bits of information so that a modem may transmit 56 kbit/s of information over a phone line with a bandwidth of only 4 kHz and a symbol rate of 8 Kbaud. A related metric which is used to measure the aggregated bandwidth of a whole network is bisection bandwidth.

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 bandwidth may be called bandwidth theft.

In discrete time systems and digital signal processing, bandwidth is related to sampling rate according to the Nyquist-Shannon sampling theorem.

When Additive white Gaussian noise is present in a digital communication channel, the Shannon-Hartley theorem gives the relationship between the channel's bandwidth, the channel's capacity, and the Signal-to-noise ratio (SNR) ratio of the system.