Bandwidth (signal processing)

For the term in linear algebra, see Sparse matrix.

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. In case of a baseband channel or signal, the bandwidth is equal to its upper cutoff frequency. Bandwidth in hertz is a central concept in many fields, including electronics, information theory, radio communications, signal processing, and spectroscopy.

In computer networking course literature and computer science publications, digital bandwidth or just bandwidth often refers to data rate measured in bits/s, for example channel capacity or network throughput. The reason is that according Hartley's law, the digital bandwidth capacity (i.e. the channel capacity) of a physical communication link is related to its bandwidth in hertz, sometimes denoted analog bandwidth in computer networking literature. For the case of high signal/noise ratio, the digital bandwidth consumption (i.e. the throughput) of a bit stream or logical link in a computer network is proportional to the average spectral bandwidth of the analog signal representing the bit stream during a studied time interval. However, measuring bandwidth in bits/s is disputed due to confusion with the original definition. Less ambiguous terms are for example gross bit rate, net bit rate, throughput, goodput or channel capacity.

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.

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.

Analog systems

A graph of a bandpass filter's gain magnitude, illustrating the concept of -3 dB (or half-power) bandwidth, at a gain of 0.707. The frequency axis of this symbolic diagram can be linear or logarithmically scaled.

For analog signals, which can be mathematically viewed as functions of time, bandwidth BW or $\Delta f$ 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 (half power $\approx -3$ dB, since $10\mathrm {log} _{10}(1/2)\approx -3$ ; see Decibel). 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 word bandwidth 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.

As an example, the (non-baseband) 3-dB bandwidth of the function depicted in the figure is $\Delta f=f_{2}-f_{1}\,$ , whereas other definitions of bandwidth would yield a different answer.

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 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 ${\frac {1}{\sqrt {2}}}$ of the maximum signal amplitude (half power).

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

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.

When a website grows in popularity or exceeds its bandwidth limits, webmasters may reduce bandwidth usage by employing bandwidth optimization techniques.

Bandwidth in business

Bandwidth has acquired a recent definition in corporate business practice. The term is used to connote capacity, manpower, energy or time (or any combination of these) in relation to the ability to perform a task.^[1]

References

^ Wiktionary definition of "bandwidth"

[1] Wiktionary definition of "bandwidth"

[1]

Overview

Analog systems

Bandwidth in web hosting

Bandwidth in business

See also

References